On Passover, Ashkenazic Jews do not eat kitniyot because kitniyot products may get confused with chametz products. The prohibition against kitniyot on Passover is only against eating it, not against possessing it.
The Sephardic community did not accept this geonic prohibition, because the main articles of food in their geographic locations were rice and legumes. Consequently, today Sephardic Jews eat kitniyot on Passover.
Furthermore, not all Ashkenazic Jews adopted the same prohibition against kitniyot on Passover. Some will not eat kitniyot derivatives, but many will use kitniyot-based oils on Passover such as corn oil and peanut oil.