Another person x Someone else: Qual a diferença

Hi folks!

I always listen to people saying "another person" as if they meant "someone else".
For instance, I prefer a private course because I don't want to study with another person.
Wouldn't it be better saying: I don't want to study with someone else?
Do both phrases (another person and someone else) have the same meaning in a case like that?

Thanks in advance!