Ways to say Friend

I know of three ways to say 'friend' in Japanese. 友達となかまと友人です。I know the difference in usage between 友達 and なかま I think. The first is more of a classmate relationship and the second is more of a long term relationship or a relationship where people get through struggles together for example.

But where does 友人 fit into the mix?

I believe there is a bit of a difference between:
友達、友人
and
なかま.

なかま is more like buddies, mates, that you associate through some activities - it may be your hobby, sports, club at school, or struggles, as you say, but the sense of belonging together to "do something" is always there.

On the other hand, 友達 is "friends," so is 友人, but this one is a bit more formal, or grown-up way of saying just about the same thing.

あーなるほど。ありがとうございます〜。