To be honest, they are quite similar.
However, you cannot use them interchangeably in the past tense!
Eg.
He always ate a lot: Correct
He forever ate a lot: Incorrect
Always is usually used when the person can control the time limit but would like to continue until the end of time. Forever has a feeling that the speaker cannot decide.
To be honest, except for the past tense, I think you can use them interchangeably (i.e. you can use forever instead of always and vice versa and it doesn't matter).
Hope this helps!