Judaism, Christianity, Islam and a few other religions (Rastafarianism for example) are part of the same family of religions, called “Abrahamic Religions”: https://en.wikipedia.org/wiki/Abrahamic_religions In Islam, “Allah” literally means “God”. It’s the same God that Jews and Christians believe in. Arab Christians call God “Allah”.

When it comes to the bible itself, “the Quran mentions the Torah, Psalms, and Gospel as being revealed by God in the same way the Quran was revealed to Muhammad” https://en.wikipedia.org/wiki/Islamic_view_of_the_Bible