Shard Convergence checks for cards with the subtypes Plains, Island, Swamp, and Mountain, not for cards with those names. You may find nonbasic land cards this way, as long as they have appropriate subtypes.

You don’t have to find all four cards.

You may find “dual lands” with Shard Convergence. The Plains card you find, for example, can have a second subtype. What subtypes it has won’t impact what other cards you can find. For example, you may find a Hallowed Fountain (which has subtypes Plains and Island) as the Plains card, and another Hallowed Fountain as the Island card.