Cart means any small conveyance while kart specifically refers to a very small race car.
Kart was made popularized by Mario-kart franchise and Go-kart racing. Cart usually has a word preceding it like shopping cart, golf cart.
Cart as a noun is a small, open, wheeled vehicle, drawn or pushed by a person or animal, more often used for transporting goods than passengers. while Kart as a noun is a go-cart.
Part of speech: verb
Definition: To carry goods.
Part of speech: noun
Definition: A small, open, wheeled vehicle, drawn or pushed by a person or animal, more often used for transporting goods than passengers. A small motor vehicle resembling a car; a go cart. A cartridge for a video game system.
Part of speech: noun
Definition: A go-cart.
We hope you now know whether to use Cart or Kart in your sentence.