Not a native speaker but I also find that odd: I always thought talented referred to the parable about the servants who were given talents, and as such I would expect that talented and gifted would be almost the same.
Disclaimer: I shouldn't be regarded as any sort of authority on the English language.
I sort of decide what words mean to me, publish them, and then stick to those definitions (while pointing anyone confused towards the published definitions).
There's probably a better way to classify these ideas without tripping over other peoples' lexicographic pedantry, but this is the Internet and you're always going to find a contrary opinion no matter what you do. The winning move is to not play.
Thus:
talent: natural affinity
skill: aptitude gained through effort
gifted: a person who is both talented and skilled in an area