Rare means unsual or uncommon. Scarce means insufficient or hard to find.

Note that "rare" almost always has positive connotations in English -- unlike its cognate in some Latin languages.

Scarce is more for something that is needed, like food or other resources, while rare could just be anything that's hard to find, like a gem or species of animal.

Anastasia, here are some examples to clarify. - Blue eyes are rare in that population of mice. - Food is scarce in the southern region of Somalia. Hope that helps.