You hold USDC on Ethereum and want the same dollars on Polygon, where a transfer costs a fraction of a cent: to use an app deployed there, to make a run of small payments without paying Ethereum gas each time, or to top up a wallet that someone else will spend from on Polygon.
Both addresses look the same — 0x and 40 characters — and that is the trap. Sending USDC from an Ethereum wallet to a Polygon address is just an Ethereum transfer to that address on Ethereum; nothing arrives on Polygon. The token has to be received on one chain and paid out on the other. Here you send once on Ethereum and USDC is transferred to you on Polygon.