Having read the threads Is SqlCommand.Dispose enough? and Closing and Disposing a WCF Service I am wondering for classes such as SqlConnection or one of the several classes
For SqlConnection, from the perspective of the connection itself, they are equivalent. According to Reflector, Dispose() calls Close() as well as doing a few additional memory-freeing operations -- mostly by setting members equal to null.
For Stream, they actually are equivalent. Stream.Dispose() simply calls Close().