My understanding (and I may be wrong there) is that prophylaxis is a wider concept than overprotection, and so there are some prophylactic moves that don't have anything to do with overprotection (like advancing one of the castling pawns to defend against 8-th line mates).

I also think I get the point of overprotection in term of enhanced piece mobility. However when it comes to prophylactic moves **not** involving overprotection (like the pawn advanced discussed above) is it really just a fancy name for not having the time to find a way to take the initiative?