Burning in crypto is covered in full in the entry Burning Tokens, which explains why projects burn tokens, how it is done and what effect it has. This page gives a short definition and explains the different word forms.
To burn a token is to remove it from circulation permanently. The usual method is to send it to a burn address whose private key is unknown, so the tokens can never be spent, or to call a smart contract function that destroys them and reduces the recorded supply. Projects burn tokens to reduce supply, to remove unsold tokens after a sale, or as part of fee mechanisms such as those described under BEP-95. Stablecoin issuers burn tokens when they are redeemed for cash, a process covered in stablecoin minting and burning. The total destroyed is tracked as burned supply.
"Burn", "burned", "burnt" and "token burn" are different forms of the same idea: "burn" is the action, while "burned" or "burnt" describes tokens or supply that have been destroyed. All refer to the same practice.