To answer your question I would say that Christians and Muslims should be worshipping the same God but unfortunately when Christians believe Jesus (pbuh) to be God, Son of God (trinity, three in one etc) then the things get confused.
As for the words “Allah” or “God” that has more to do with language you speak. Jesus did not speak English so he surely did not call his God, “God”.
But I will clarify it in a different way. Jews, Christians and Muslims should all be worshipping the God their Prophets worshipped instead of adding the prophets in that list. If they do so then things will be very simple.