In general, there are two fundamental approaches to kashrut on Pesaĥ. According to most poskim, the laws of ĥametz on Pesaĥ are no different than the laws of all other forbidden foods, with one exception: all other forbidden foods are batel be-shishim (rendered insignificant when constituting less than one sixtieth of the volume of a mixture), whereas ĥametz is not. However, all other laws of mixtures apply to ĥametz on Pesaĥ. Therefore, when there is no halakhic reason to suspect that a food mixture has absorbed the taste of ĥametz, it is kosher for Pesaĥ. Likewise, where an individual posek is stringent and the great majority of poskim are lenient, halakha follows the lenient opinion.
However, Ashkenazic Jews are customarily very strict about ĥametz, often showing concern for a stringent opinion even against the lenient majority and practicing caution where general halakhic principles indicate no reason to do so. Nevertheless, Ashkenazic custom also places a limit to its stringencies, and poskim are careful not to pile restrictions upon existing restrictions. The general tendency, though, is to show concern for every uncertainty. The basis for this approach is the Sages’ ruling that even a drop of ĥametz is forbidden; thus, if a mere crumb of ĥametz renders its entire mixture forbidden, so too individual halakhic opinions should be taken into account.
This explains the consistent difference between the rulings of Shulĥan Arukh, which follow general halakhic principles, and those of Rema, which account, le-khatĥila, for the stringent opinions. Nonetheless, in cases of pressing need Rema adopts the lenient approach, since halakha fundamentally accords with most poskim.
In general, Sephardim follow Shulĥan Arukh and Ashkenazim follow Rema. However, some Sephardic poskim tend to be stringent, and their rulings are accepted in some Sephardic communities.