The Geonim were Babylonian rabbis who taught Talmud and decided on issues on which no ruling had been rendered during the period of the Talmud. "Geon" is Hebrew for "genius."
The Rishonim were the leading rabbis between approximately 1250 to 1550, that is in the era before the writing of the Shulkhan Arukh by Rabbi Yosef Karo, which is considered the most authoritative compilation of Jewish law since the Talmud.
