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God is the word used in Christianity, it is the actual word .... Allah is the actual word used in Islam
God is the word used in English, Allah is used in Arabic. When English people speak about the Islamic god, they use "God" too, just like they do for the gods of any other religion.
the transliteration, is Arabic, the translation is of Arabic
the etymologies are different, the two words are of different cultures - Islam isn't Christianity because the two are religions, the original is of Arabic culture, belongs to Arabic culture:
the two words root differently by way of their different etymologies, and accordingly have different meanings which are possessed by the different pronunciations, which stem from the languages they evolved in
please see God#Etymology_and_usage at Wikipedia