REBUILD - Clustered Index, TABLE, or both? I'm having trouble finding a definitive resource on this anywhere, so hopefully a guru can give me an answer here.

I have a very large table that we had to add a column to.  The clustered index is pretty highly fragmented, and I want to do an ALTER INDEX REBUILD to clean it up.

I also normally do an ALTER TABLE REBUILD when I change the columns since this cleans up any pointers or splits from that operation.

Do I need to do both since we are talking about a the clustered index, which is essentially the table?

My suspicion is the ALTER INDEX REBUILD on the clustered will not update everything that the ALTER TABLE will, but I also am afraid that the ALTER TABLE won't clean up the index fragmentation.
If you rebuild the clustered index there shouldn't be any need to rebuild the table.  If the table was a heap (didn't have a clustered index) then you might want to rebuild it.