The two are often used interchangeably.
That said, a Google search of "seasoned by experience" (in quotes) comes up with many examples of that phrase being used by legitimate publications, including by some dictionaries in the example sentences attributed to seasoned.
This points to the fact that the two words can have different implications. Seasoned really means something closer to matured. Because people typically mature as a result of experience, the conflation of the two words is understandable. However, there are plenty of people out there who've had a world of experience and have yet to grow up.