Do Islam and Christianity have different origins?

No. Together with Judaism, they go back to the prophet and patriarch Abraham, and
their three prophets are directly descended from his sons Muhammad from the eldest,
Ishmael, and Moses and Jesus from Isaac. Abraham established the settlement which
today is the city of Makkah, and built the Ka’abah towards which all Muslims turn
when they pray.

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“All humans are dead except those who have knowledge; and those who have knowledge are asleep, except those who do good deeds; and those who do good deeds are deceived, except those who are sincere; and those who are sincere are always in a state of worry.” Imam Shafi (RH)