The right (left) ideals, quasi- and bi-ideals play an essential role in studying the structure of some ordered semigroups. In an attempt to show how similar is the theory of ordered semigroups based on ideals or ideal elements with the theory of ordered semigroups based on fuzzy ideals, keeping the usual definitions of fuzzy right ideal, fuzzy left ideal, fuzzy quasi-ideal and fuzzy bi-ideal, we show here that in ordered groupoids, the fuzzy right (resp. left) ideals are fuzzy quasi-ideals and in ordered semigroups, the fuzzy quasi-ideals are fuzzy bi-ideals. Moreover, we prove that in regular ordered semigroups, the fuzzy quasi-ideals and the fuzzy bi-ideals coincide. We finally show that in an ordered semigroup the fuzzy quasi-ideals are just intersections of fuzzy right and fuzzy left ideals.