Christians v.s. Catholics

If Catholics prayed to their God...would it the same God as christians? And would they be answered? Does God hear their prayers?

Can it be paralleled to the muslim God (Allah), which being...not the same.

Because I figured if the core values/doctrine of catholic is different from being christian (mainly, that of salvation. One is though works, the other is through faith & grace), then would the God be the same? Would we be worshiping the same God? Hence, would prayer be heard from the same God? Or, there is only one God...

When one part of it changes...it is no longer whole and complete, if there are differences at all, I mean...it's the word of God. Imagine, if little things could be changed in there..what does that make it...

My intial answer/thought would be "no", but i just want to confirm...