How To: Some definitions of ArcSDE 8 basic terms for SDE 3 users
An ArcSDE 8 feature class is somewhat equivalent to a layer in SDE 3.x. Information about a feature class is stored in the table SDE.LAYERS and in tables it refers to, such as SDE.SPATIAL_REFERENCES.
A description of how a feature class has been projected and stored. It includes the x/y offset and scale, the m and z offsets and scales, and the coordinate reference. A spatial reference is stored in the table SDE.SPATIAL_REFERENCE and is referred to by an integer, the SRID (spatial reference ID). A single spatial reference can be used by multiple feature classes.
A collection of feature classes that share a spatial reference. Feature datasets cannot contain other feature datasets; they are not able to be nested.
Geodatabases contain feature classes and feature datasets. It is somewhat equivalent to an SDE 3.x instance. To be a geodatabase, an ArcSDE instance must have the metadata tables which are created by running the tool gdbs.