What is the difference between a variant and a variation?

Very strictly speaking, variation is change, and a variant is one of the forms resulting from the change.

The use of variation to mean variant is so common, though, that only a hardcore pedant would ever even recognize a difference in that context, much less say either one is incorrect.

Coming from a technical perspective, if I report that I tackled a problem using a variant of Algorithm A, then this variant is most likely one that other people have used before and there is literature on its use. If instead I say I was using a variation of Algorithm A, then the existing variants of Algorithm A didn't meet the particular requirements of my problem and I therefore needed to create my own adaptation. People after me might decide to call this a variant of Algorithm A, if they deem it close enough to the original.

Caution: I'm not a native English speaker.

A variation is something that differs from a standard or from something considered normal, while a variant differs from other things in its own class--that is, it's not something that necessarily differs from a norm or standard. Source: Garner's Modern American Usage.