What is a SQL Server Distributor? This question (SQL Server transactional replication distributor), mentions a blog post HERE, which talks about how the distribution database works in relation to publishers and subscribers. Seems pretty clear.

Is the Distributor a fully fledged instance of SQL Server? I understand that it could run on a separate server, so it would seem like it. If not, what is the difference between a Distribution server and a SQL Server instance?

I guess from THIS article that the transaction logs of the publisher are stored in the distribution database, which are then read by the subscribers. And that this is called 'transactional replication'? Are there any other types of replication?
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.