When we just close something it creates two-way links between the threads and stops people answering the duplicate. That's about it.
When we do a merge, all the answers from the duplicate are moved into the master question. The dupe is locked (no more comments, votes, etc).
If an answer on a dupe is accepted, a merge will unset this, it won't become an accepted answer on the master thread. Any accepted answer on the master thread is unaffected but the OP may wish to change it based on the quality of the merge.
We don't merge as often as we could. We only do it when we feel there are answers of quality worth saving. Answers on duplicates are often duplicates themselves so there's little reason in pulling them over.