Stereotypically a "genius" pianist is one who has studied music theory, and has the intellect to know who Mozart was, and etc, and then combines that knowledge, and years of study with his muscular finger control to be able to play piano with virtuosity.
Then some slobbering kid come along who cant even speak, nor read music, cant even read words, nor dress themselves, but sits at the piano and just plays Mozart, or Wagner, or Duke Ellington, or whomever, perfectly by ear from just hearing it one time. The former is the "genius" and the latter is "the savant". The latter is a freaky thing that baffles the experts.
But I suspect that the two things over lap. Many celebrated geniuses like Newton and Einstein were deficient in other mental realms, and though learned were probably also somewhat savant-like.