Hi akimhaneul,
You're right that the concepts seem pretty similar, but there is a key difference. Source monitoring describes the cognitive process of keeping track of where you got information from, and a source monitoring error happens if you get it wrong. In contrast, source amnesia refers to just not knowing the source of the information. You don't even have to be trying -- the idea is that you have source amnesia if you're unable to recall where you found out about something.
Hope this helps & good luck!