As nouns the difference between cartwright and wheelwright

is that cartwright is a person who makes carts; a wainwright while wheelwright is a person who builds and repairs wheels, especially wooden spoked ones.

As proper nouns the difference between cartwright and wheelwright

is that cartwright is {{surname|A=An|English occupational|from=occupations}} for someone who made carts while Wheelwright is {{surname|comparatively rare English occupational|from=occupations}} for someone who made wooden wheels.