And even if you just call them islands, you'll run into ambiguous territory somewhere. Is Manhattan really an island? If so, then is Harlem River really a river? (and there are also islands which become part of the mainland at low tide)

BTW, the state of Rhode Island was originally "the State of Rhode Island and Providence Plantations" which made sense but was unwieldy. Now the actual island of Rhode Island is called Aquidneck Island.