Like erc20, when someone sends me a erc20 token, they're not actually sending the tokens to my address. Instead, they're sending a transaction to the Ethereum network that calls the transfer function of the ERC-20 contract with your address as the recipient and the amount of tokens to transfer.
The ERC-20 contract then updates its mapping of token balances, which records the number of tokens held by each address. This means that the balance of ERC-20 tokens associated with my address increases accordingly.
Does the same happen in the case of erc721?