Well, God is Allah. The name means exactly the same thing,
No, it does not mean the exact same thing.
Ever heard of the Shahada?
لا إله إلا الله، محمد رسول الله
There is no god but Allah, and Mohammed is his prophet
الله God, Allah, father, the Creator, maker
إله god, divinity
الإله god
رب God, god, lord
معبود god, idol, fetish, divinity
الخالق creator, the Creator, God, maker, author, former
حاكم قوي god
خالق god
Allah is a proper noun, just as is Yahweh, Adonai, Elohim, Jehovah, etc.
We use the term "God" as a proper noun, but it is not equivalent to Allah. Allah is specifically assigned as the designation for the Muslim deity.