The difference is purely contextual, something can be both small and tiny. Tiny will often import the idea it is unusually small, into the meaning. However, they do not describe specific sizes on thier own.

"Tiny" means "very small". A "small difference" might be as much as 10%, while a "tiny difference" could be 1% or less.

Tiny can imply small and cute: A tiny baby, a tiny kitten.