The words axel, axil, axle sound the same but have different meanings and spellings. Why do axel, axil, axle sound the same even though they are completely different words?
The answer is simple: axel, axil, axle are homophones of the English language.
A jump in figure skating that is initiated from the outer forward edge of one skate, followed by one and one-half midair turns and a return to the outer backward edge of the other skate.
The upper angle between a lateral organ, such as a leafstalk, and the stem that bears it.
A supporting shaft or member on or with which a wheel or a set of wheels revolves.
The spindle of an axletree.
Either end of an axletree.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.
If they are spelled the same then they are also homographs (and homonyms); if they are spelled differently then they are also heterographs (literally "different writing").