What is a SQL Server Distributor?
Yes the Distributor is a "fully fledged instance of SQL Server". A Distributor is a SQL Server instance that contains a distribution database. The Distribution server could have other databases on it.

The transaction logs of the publisher are NOT stored in the distribution database. What gets stored in there are the DML commands (INSERT/UPDATE/DELETE), though represented a bit different.

The other types of replication are Merge, Snapshot and Peer to Peer.