They mean the same thing but 'after' cannot stand alone, 'then' and 'afterwards' can only stand alone: 'I went to the party, after THAT, I went home'________'I went to the party, then I went home'_________'I went to the party, afterwards I went home' ------------------ if you say 'I went to the party after I went home' it means you went home first and THEN went to the party.