When people think Savant, they usually think of "idiot savants" who are people with extraordinarily gifted kills in a particular area while their general skills are at or below average. They are, in some cases, algorithmic machines who can, for example, tell you the day of the week of a particular date. Their gifts are organic in that they are the result of Nature, not Nurture.
A Genius chooses their area of specialization. They're general purpose machines. They can bore you to death on a wide variety of subjects, and they can tell you, or deduce, the algorithm for determining the day of the week from the date.
A Savant can easily be stumped, a Genius conceals their ignorance better.