A person says he's Jewish. Deeper inquiry reveals that there are sheilos. For Halachically significant areas (e.g. aliyas, minyanim), he's not considered Jewish. But what's the difference between a person who is not Jewish and a person for whom there is a sheiloh that they are Jewish. Are the latter usually from mixed families, and that there is murkiness even though overall it's Jewish. Is the latter more of an honest mistake? A person who claims to be Jewish when there is a sheilah, is he considered a liar?
Someone who is definitely non-Jewish can marry another non-Jew, and has no obligation to keep the specific commandments of Jews. Someone who might be Jewish and might not can't really marry anyone: they can't marry a Jew because they might be non-Jewish, and they can't marry a non-Jew because they might be Jewish. And whether and how they keep the commandments applying to Jews would be a tricky question a competent rabbi would have to answer for their specific circumstances.