Axis, Axle

Axis and axle have come to us almost unchanged from their origins 6,000 years ago. Both words have their origin in the Proto-Indo-European (PIE) aks (axis).
 
Axis
 
The word axis (an imaginary motionless straight line around which a body rotates) came to English in the 1540s from Latin axis and PIE aks. PIE aks is also the source of words such as Old English eax, Old High German ahsa (axle), Greek axon, Sanskrit aksah, and Lithuanian asis—all meaning axis.
 
Axle
 
The word axle (a pole or pin upon which a wheel revolves) came to English in the 1630s from Middle English axel, Old English eax, and Old Norse oxull. These words come from Proto-Germanic akhsulaz and PIE aks.
 
 
In brief, axis comes to English from PIE via Latin sources; axle comes to English from PIE via Germanic sources.
 
Image: The Ljubljana Marches Wheel with axle is the oldest wooden wheel yet discovered (c. 3,130 BCE).

Reference: Online Etymological Dictionary, https://www.etymonline.com/