wheel vs cartwheel

wheel and cartwheel both are nouns.

Word	Noun	Adjective	Verb	Adverb
wheel	Yes	No	Yes	No
cartwheel	Yes	No	Yes	No

As nouns, cartwheel is a hyponym of wheel; that is, cartwheel is a word with a more specific, narrower meaning than wheel:

wheel: a simple machine consisting of a circular frame with spokes (or a solid disc) that can rotate on a shaft or axle (as in vehicles or other machines)
cartwheel: a wheel that has wooden spokes and a metal rim

As verbs, cartwheel is a hyponym of wheel; that is, cartwheel is a word with a more specific, narrower meaning than wheel:

wheel: change directions as if revolving on a pivot
cartwheel: do cartwheels: perform an acrobatic movement using both hands and feet

wheel (noun)	cartwheel (noun)
a simple machine consisting of a circular frame with spokes (or a solid disc) that can rotate on a shaft or axle (as in vehicles or other machines)	acrobatic revolutions with the body turned sideways and the arms and legs outstretched like the spokes of a wheel
a circular helm to control the rudder of a vessel	a wheel that has wooden spokes and a metal rim
an instrument of torture that stretches or disjoints or mutilates victims	a dollar made of silver
game equipment consisting of a wheel with slots that is used for gambling; the wheel rotates horizontally and players bet on which slot the roulette ball will stop in
a handwheel that is used for steering
a wheeled vehicle that has two wheels and is moved by foot pedals
forces that provide energy and direction

wheel (verb)	cartwheel (verb)
change directions as if revolving on a pivot	do cartwheels: perform an acrobatic movement using both hands and feet
move along on or as if on wheels or a wheeled vehicle
wheel somebody or something
ride a bicycle