Suppose Chris says, “Gordon is married,” and Malcolm says, “Gordon is a bachelor.” Has Malcolm contradicted Chris? It depends on whether Malcolm is referring to the same ‘Gordon’. If Malcolm is talking about some other ‘Gordon’, there’s no contradiction. Conversely, if you think Malcolm has contradicted Chris, you’re presupposing that they’re talking about the same ‘Gordon’.
Now suppose you think, as is plausible, that when the Quran says that God has no son (Q4:171; Q6:101) it’s contradicting the Bible (John 3:16, etc.). In that case, you’re presupposing that the Quran is referring to the same God as the Bible. Conversely, if you think the Quran is referring to a fictional, non-existent deity when it says that God has no son, you need to consider whether the Quran is actually contradicting the Bible in saying so (and if it is contradicting the Bible, how it is doing so). The same goes for other objectionable statements the Quran makes about God.
If you say the Quran is in fact referring to the God of the Bible (because it make false claims about the God of the Bible) are you thereby implying that Christians and Muslims “worship the same God”? Not necessarily. It all depends what you mean by “worship the same God”.