Axel and Axle are two different nouns, although you are more likely to see axel as a misspelling of axle, than as its own word, because the real word axel has a very specific meaning.
Axle, the more common word, refers to a (usually metal) shaft—shaped like a straight pipe or rod—that goes through the centers of wheels, usually joining two wheels; most cars have a front axle and a rear axle. Trucks tend to have more. Don’t confuse axle with axis, which has a related but more abstract meaning:
Our car hit a pothole and it broke the front axle!
Axel, on the other hand, is not just a misspelling of axle; it is also the name of a specific movement in figure skating—a combination of jumping and spinning at the same time:
She performed an almost perfect axel on only her second atttempt.