You can have biological parents, adoptive parents, foster parents and step-parents(ditto for siblings). In-laws is somewhat similar. In terms of blood relatives, I'd think of it as 1st, 2nd or 3rd degree incest--parent-child, sibling-sibling is 1st degree; cousin-cousin, aunt-nephew, grandparent-grandchild is 2nd degree; 2nd cousins, great-aunt/greatnephew, great-grandparent/great grandchild(ew!) would be 3rd degree. I think half-siblings would still be 1st degree(ish).
If you have non-biological parents who raised you from an early age, they're functionally your "real parents". I don't think anyone who felt attraction to such parents would characterize those feelings as non-incestuous.