Genius, as far as I can tell, relates to intelligence. There are many different types of intelligence and as far as I can tell being a savant does not really involve a great deal of intellect.
I was always quick at maths, in school I never understood why others found it so hard, I mean, it's not like something you have to actually think about. You read an equation, your brain supplies an answer and you write the answer down. Not real hard. To me it was just a function that my brain did by itself, it was never anything I had to think about.
My sister was hopeless at her schoolwork, especially with maths, but she was always far smarter than I could ever hope to be.
The true measure of intellect is how quickly people learn from mistakes. The truly intelligent learn from seeing other people make mistakes and avoid the same fates for themselves. To me a mark of genius is someone who never makes the same mistake twice.
Einstein once described insanity as "repeating the same process again and again hoping to achieve a different result".