Both READ_COMMITTED_SNAPSHOT ON and ALLOW_SNAPSHOT_ISOLATION ON
From a previous answer to this:


  If you use ALLOW_SNAPSHOT_ISOLATION make sure you use SET
  TRANSACTION ISOLATION LEVEL SNAPSHOT in your code, otherwise you will
  not get any of the benefits.
  
  If you set SET READ_COMMITTED_SNAPSHOT ON, then there is no need to
  modify any code. MS SQL Server automatically applies snapshot
  isolation for that table.


Basically, with only ALLOW_SNAPSHOT_ISOLAION, you still have to specify the isolation level in the query/SP to make it use that isolation level.

With READ_COMMITTED_SNAPSHOT set to ON, the DB is automatically in that mode and there's no need to modify your queries.

ALLOW_SNAPSHOT_ISOLATION and READ_COMMITTED_SNAPSHOT

In the answer I linked to above, there is a link to Kim Tripp's video on snapshot isolation.  It's pure gold.