I heard someone say that Christianity started out as Jewish heresy and over a period of decades it became a completely separate religion. I think that generalization has some merit.
Also Judaism evolved into something different as well. In some ways rabbinic Judaism didn’t settle itself and become the dominant approach of Jews until after the contours of what would become catholic Christianity were already in place. The Mishnah is from 150 CE, the Talmuds are from 400-600 CE. We’re looking at sister religions that both emerged out of the ashes of the Second Temple – not a mother and her daughter.