The thirty-oared ship is the triaconter. You are correct that it is much smaller than a trireme. The triaconter and penteconter (often spelled more accurately as triakonter and pentakonter), its larger fifty-oared cousin, were developed earlier than the trireme. They did not have the multiple sets of oars or the combat decking of the classical trireme.

This may answer your question, but I or other folks around are happy to expand if you have any follow-up questions.