They married descendents of Rachel, Leah, Bilhah, and Zilpah... ;) Just kidding. Good question.
I have a very goy question. Are the Ashkenazim the Hasidim? Or are they something different? I'm just surprised to hear one type of Jew constitute half of the Jewish population. Or is Ashkenazim a bloodline more than a religious practice? And some Ashkenazim are Orthodox, some Conservative, some Reformed, etc.?
Oops. Now I see in the title it says Ashkenazim are European Jews! Was that there the whole time? I must be getting old. And tired.
The difference today is mostly in slight differences in religious observance and traditions. Arising out of different Rabbinical authority interpretations.
Communities from various places kept those differences so they account for certain different ethnic Jews being one or the other.
My family history should make us Sephardi but a zig zag in and out of Easter Europe starting about 500 years ago makes us Ashkenazi.
The answer to your last question is yes.
Ashkenazi Jews are those of European descent; Sephardic Jews are from Spain, North Africa and the Mid East-recently, of course, as all Jews except converts and their descendants are originally of Mid Eastern origin. BTW, Ashkenaz is Germany and Sepherad is Spain - that is the origin of these terms.
Religious practice is not genetic or familial in origin - it is up to each person what they do. There are Orthodox, Conservative and Reform Jews who are Ashkenazi, just as members of all three groups can be Sephardic. The Hasidim are almost all Ashkenazi Jews, but relatively few Ashkenazi Jews are Hasidim.