Quran says that yeah it's the same God tho,but...there are some disagreements too.
Yes but the Quran aims to correct Christianity in regard to some of its beliefs about God (e.g the Incarnation, the Trinity etc.). These points are fundamental for Christianity, and you can't conceive of the Christian concept of God as lacking at least those features. Conversely, Islam maintains that God is not triune and has never incarnated, and those beliefs too are fundamental for Islam. So in this sense, the answer would be no: Christians and Muslims do not worship the same God.
On the other hand both Christianity and Islam identify God as the God who spoke to Abraham, Moses and the other prophets, and both of them would be unimaginable without those accounts, so in this sense the answer would be yes: Christians and Muslims do worship the same God.
Of course you could go to some esoteric, "restorationist" or syncretic movement within both Christianity and Islam and find non-trinitarian Christians like Oneness Pentecostals or "trinitarian" Muslims like the Alawites, but I suppose that it's the orthodox forms of the religions that matter.