Answer:
The correct answer is that Allah is not related to the Gods of Christians and Jews. The religions on basis are completely different. The only similarity is between teachings (and the only real similarity between Judaism and Christianity is the Old Testament). Now, that does not mean that the religions do not share the similarities. Both Allah and Yahweh/Elohim are the only God in their respective religions (monotheism). Both had a period of religious growth through conquest (though misinformed for both through their principal religious groups).
“Go, therefore, and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe everything I have commanded you. And remember I am with you always, to the end of the age.” – Matthew 28:19-20 (Bible, CSB version.)
"Therein they will hear no abusive speech, nor any talk of sin, only the saying, 'Peace, peace.'" - Qur'an 56: 52-26.
Simply put, the teachings in both are relatively similar, though there may be differences found particularly in how to practice the respective religions. However, both share a monotheistic origin, and both have a major prophet (Jesus, the son of God for Christians, and Muhammed the prophet for Muslims).
You can learn more about this topic through the Bible (for Christians), Torah (for Jews), or Qur'an (for Islam).
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