Spatial Data Types Overview
There are two types of spatial data. The geometry data type supports planar, or Euclidean (flatearth), data. The geometry data type both conforms to the Open Geospatial Consortium (OGC) Simple Features for SQL Specification version 1.1.0 and is compliant with SQL MM (ISO standard).
In addition, SQL Server supports the geography data type, which stores ellipsoidal (roundearth) data, such as GPS latitude and longitude coordinates.
Important 

For a detailed description and examples of spatial features introduced in SQL Server 2012, including enhancements to the spatial data types, download the white paper, New Spatial Features in SQL Server CodeNamed "Denali". 
The geometry and geography data types support sixteen spatial data objects, or instance types. However, only eleven of these instance types are instantiable; you can create and work with these instances (or instantiate them) in a database. These instances derive certain properties from their parent data types that distinguish them as Points, LineStrings, CircularStrings, CompoundCurves, Polygons, CurvePolygons or as multiple geometry or geography instances in a GeometryCollection. Geography type has an additional instance type, FullGlobe.
The figure below depicts the geometry hierarchy upon which the geometry and geography data types are based. The instantiable types of geometry and geography are indicated in blue.
As the figure indicates, the ten instantiable types of the geometry and geography data types are Point, MultiPoint, LineString, CircularString, MultiLineString, CompoundCurve, Polygon, CurvePolygon, MultiPolygon, and GeometryCollection. There is one additional instantiable type for the geography data type: FullGlobe. The geometry and geography types can recognize a specific instance as long as it is a wellformed instance, even if the instance is not defined explicitly. For example, if you define a Point instance explicitly using the STPointFromText() method, geometry and geography recognize the instance as a Point, as long as the method input is wellformed. If you define the same instance using the STGeomFromText() method, both the geometry and geography data types recognize the instance as a Point.
The subtypes for geometry and geography types are divided into simple and collection types. Some methods like STNumCurves() work only with simple types.
Simple types include:
Collection types include:
The two types of spatial data often behave quite similarly, but there are some key differences in how the data is stored and manipulated.
How connecting edges are defined
The defining data for LineString and Polygon types are vertices only. The connecting edge between two vertices in a geometry type is a straight line. However, the connecting edge between two vertices in a geography type is a short great elliptic arc between the two vertices. A great ellipse is the intersection of the ellipsoid with a plane through its center and a great elliptic arc is an arc segment on the great ellipse.
How circular arc segments are defined
Circular arc segments for geometry types are defined on the XY Cartesian coordinate plane (Z values are ignored). Circular arc segments for geography types are defined by curve segments on a reference sphere. Any parallel on the reference sphere can be defined by two complementary circular arcs where the points for both arcs have a constant latitude angle.
Measurements in spatial data types
In the planar, or flatearth, system, measurements of distances and areas are given in the same unit of measurement as coordinates. Using the geometry data type, the distance between (2, 2) and (5, 6) is 5 units, regardless of the units used.
In the ellipsoidal, or roundearth system, coordinates are given in degrees of latitude and longitude. However, lengths and areas are usually measured in meters and square meters, though the measurement may depend on the spatial reference identifier (SRID) of the geography instance. The most common unit of measurement for the geography data type is meters.
Orientation of spatial data
In the planar system, the ring orientation of a polygon is not an important factor. For example, a polygon described by ((0, 0), (10, 0), (0, 20), (0, 0)) is the same as a polygon described by ((0, 0), (0, 20), (10, 0), (0, 0)). The OGC Simple Features for SQL Specification does not dictate a ring ordering, and SQL Server does not enforce ring ordering.
In an ellipsoidal system, a polygon has no meaning, or is ambiguous, without an orientation. For example, does a ring around the equator describe the northern or southern hemisphere? If we use the geography data type to store the spatial instance, we must specify the orientation of the ring and accurately describe the location of the instance. The interior of the polygon in an ellipsoidal system is defined by the lefthand rule.
When the compatibility level is 100 or below in SQL Server 2014 then the geography data type has the following restrictions:

Each geography instance must fit inside a single hemisphere. No spatial objects larger than a hemisphere can be stored.

Any geography instance from an Open Geospatial Consortium (OGC) WellKnown Text (WKT) or WellKnown Binary (WKB) representation that produces an object larger than a hemisphere throws an ArgumentException.

The geography data type methods that require the input of two geography instances, such as STIntersection(), STUnion(), STDifference(), and STSymDifference(), will return null if the results from the methods do not fit inside a single hemisphere. STBuffer() will also return null if the output exceeds a single hemisphere.
In SQL Server 2014, FullGlobe is a special type of Polygon that covers the entire globe. FullGlobe has an area, but no borders or vertices.
Outer and inner rings not important in geography data type
The OGC Simple Features for SQL Specification discusses outer rings and inner rings, but this distinction makes little sense for the SQL Server geography data type; any ring of a polygon can be taken to be the outer ring.
For more information on OGC specifications, see the following:
Three instantiable types can take circular arc segments: CircularString, CompoundCurve, and CurvePolygon. A circular arc segment is defined by three points in a two dimensional plane and the third point cannot be the same as the first point.
Figures A and B show typical circular arc segments. Note how each of the three points lie on the perimeter of a circle.
Figures C and D show how a line segment can be defined as a circular arc segment. Note that three points are still needed to define the circular arc segment unlike a regular line segment which can be defined by just two points.
Methods operating on circular arc segment types use straight line segments to approximate the circular arc. The number of line segments used to approximate the arc will depend on the length and curvature of the arc. Z values can be stored for each of the circular arc segment types; however, methods will not use the Z values in their calculations.
Note 

If Z values are given for circular arc segments then they must be the same for all points in the circular arc segment for it to be accepted for input. For example: CIRCULARSTRING(0 0 1, 2 2 1, 4 0 1) is accepted, but CIRCULARSTRING(0 0 1, 2 2 2, 4 0 1) is not accepted. 
LineString and CircularString comparison
The following diagram shows identical isosceles triangles (triangle A uses line segments to define the triangle and triangle B uses circular arc segments to defined the triangle):
This example shows how to store the above isosceles triangles using both a LineString instance and CircularString instance:
DECLARE @g1 geometry; DECLARE @g2 geometry; SET @g1 = geometry::STGeomFromText('LINESTRING(1 1, 5 1, 3 5, 1 1)', 0); SET @g2 = geometry::STGeomFromText('CIRCULARSTRING(1 1, 3 1, 5 1, 4 3, 3 5, 2 3, 1 1)', 0); IF @g1.STIsValid() = 1 AND @g2.STIsValid() = 1 BEGIN SELECT @g1.ToString(), @g2.ToString() SELECT @g1.STLength() AS [LS Length], @g2.STLength() AS [CS Length] END
Notice that a CircularString instance requires seven points to define the triangle, but a LineString instance requires only four points to define the triangle. The reason for this is that a CircularString instance stores circular arc segments and not line segments. So the sides of the triangle stored in the CircularString instance are ABC, CDE, and EFA whereas the sides of the triangle stored in the LineString instance are AC, CE, and EA.
Consider the following code snippet:
SET @g1 = geometry::STGeomFromText('LINESTRING(0 0, 2 2, 4 0)', 0); SET @g2 = geometry::STGeomFromText('CIRCULARSTRING(0 0, 2 2, 4 0)', 0); SELECT @g1.STLength() AS [LS Length], @g2.STLength() AS [CS Length];
This snippet will produce the following results:
LS LengthCS Length 5.65685…6.28318…
The following illustration shows how each type is stored (red line shows LineString @g1, blue line shows CircularString @g2):
As the illustration above shows, CircularString instances use fewer points to store curve boundaries with greater precision than LineString instances. CircularString instances are useful for storing circular boundaries like a twentymile search radius from a specific point. LineString instances are good for storing boundaries that are linear like a square city block.
LineString and CompoundCurve comparison
The following code examples show how to store the same figure using LineString and CompoundCurve instances:
SET @g = geometry::Parse('LINESTRING(2 2, 4 2, 4 4, 2 4, 2 2)'); SET @g = geometry::Parse('COMPOUNDCURVE((2 2, 4 2), (4 2, 4 4), (4 4, 2 4), (2 4, 2 2))'); SET @g = geometry::Parse('COMPOUNDCURVE((2 2, 4 2, 4 4, 2 4, 2 2))');
or
In the examples above, either a LineString instance or a CompoundCurve instance could store the figure. This next example uses a CompoundCurve to store a pie slice:
SET @g = geometry::Parse('COMPOUNDCURVE(CIRCULARSTRING(2 2, 1 3, 0 2),(0 2, 1 0, 2 2))');
A CompoundCurve instance can store the circular arc segment (2 2, 1 3, 0 2) directly whereas a LineString instance would have to convert the curve into several smaller line segments.
CircularString and CompoundCurve comparison
The following code example shows how the pie slice can be stored in a CircularString instance:
DECLARE @g geometry; SET @g = geometry::Parse('CIRCULARSTRING( 0 0, 1 2.1082, 3 6.3246, 0 7, 3 6.3246, 1 2.1082, 0 0)'); SELECT @g.ToString(), @g.STLength();
To store the pie slice using a CircularString instance requires that three points be used for each line segment. If an intermediate point is not known, it either has to be calculated or the endpoint of the line segment has to be doubled as the following snippet shows:
SET @g = geometry::Parse('CIRCULARSTRING( 0 0, 3 6.3246, 3 6.3246, 0 7, 3 6.3246, 0 0, 0 0)');
CompoundCurve instances allow both LineString and CircularString components so that only two points to the line segments of the pie slice need to be known. This code example shows how to use a CompoundCurve to store the same figure:
DECLARE @g geometry; SET @g = geometry::Parse('COMPOUNDCURVE(CIRCULARSTRING( 3 6.3246, 0 7, 3 6.3246), (3 6.3246, 0 0, 3 6.3246))'); SELECT @g.ToString(), @g.STLength();
Polygon and CurvePolygon comparison
CurvePolygon instances can use CircularString and CompoundCurve instances when defining their exterior and interior rings. Polygon instances cannot use the circular arc segment types: CircularString and CompoundCurve.