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?