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Why does the metadata show the coordinate system as a map projection instead of State Plane?
Several coordinate systems for the State Plane grid system are provided with ArcGIS. Looking at the properties of a State Plane coordinate system you can see it uses a map projection with parameters that are appropriate for the region. The coordinate system's projection is not State Plane; for the zones in California it is Lambert Conformal Conic. Also, the zone number is not a parameter of the coordinate system. Only the coordinate system's name identifies the grid zone to which it applies.
With the FGDC metadata standard, map projections, such as Lambert Conformal Conic, are documented by listing their parameters. For grid systems, such as State Plane, the zone is to be specified in addition to the map projection parameters. When ArcCatalog automatically generates FGDC metadata it examines the coordinate system's name to see if it is a State Plane coordinate system; if so, it extracts the zone number from the name and records the projection in the metadata following the State Plane rules.
However, several State Plane coordinate systems have been added to ArcGIS that have not been incorporated into the lookup list used by the metadata system. If the metadata system does not recognize the name as being State Plane, the coordinate system will be documented as a map projection rather than a grid system. It is important to realize that this behavior is not wrong. The coordinate system is a map projection, not a grid system. However, this does mean that the State Plane grid zone will not be recorded in the expected FGDC metadata element.