Ashkenazim are Jews of Central and Eastern Europe who speak Yiddish (Judeo-German with Hebrew, Aramaic, and Slavic influences) and follow the Jewish religion (a monotheistic religion based on the Mosaic tradition and Rabbinical commentary as described in the Torah and Talmud). They claim to be (partially at least) descended from the Ancient Israelites of the Middle East, and generally only marry other Jews and are separate from their host populations (i.e. if an Ashkenazi Jew lives in Poland, he will not be that involved in non-Jewish Polish soceity)
Non-Ashkenazi is a broad term really. I do not know if you mean Jews of other places (e.g. Sephardi Jews of Spain, Turkey and North Africa, Mizrahi Jews of the Middle East, Yemenite Jews, etc.) or non-Jewish central and Eastern Europeans.
Sephardi Jews traditionally come from Spanish speaking countries: Spain, Morocco. Jews from Portugal and Italy are also often considered Sephardi.
Ashkenazi Jews traditionally come from Eastern Europe.
There are also Mizrachi Jews. Mizrachi means 'East' and refers to Jews from the Middle Eastern and North African countries outside of of Israel.
The main difference, aside from language, are food culture and how some religious practices are observed.
An Ashkenazi is an alternative term for an Ashkenazi Jew, a group of Jews of German and Eastern European origin.
The Brothers Ashkenazi was created in 1936.
Meir Ashkenazi died in 1567.
David Ashkenazi died in 1997.
David Ashkenazi was born in 1915.
Léon Ashkenazi died in 1996.
Isaac Ashkenazi was born in 1957.
Tzvi Ashkenazi died in 1718.
Tzvi Ashkenazi was born in 1656.
Menachem Ashkenazi died in 2000.
Menachem Ashkenazi was born in 1934.
Adi Ashkenazi is 160 cm.