What is a Polygon wallet?
A Polygon wallet is an app that holds the private keys to an address on the Polygon network. The coins themselves never leave the blockchain. What the wallet holds is the key that lets you move them, which is why the recovery phrase matters more than the app you happen to be using.
Polygon PoS is a network built to scale Ethereum. It runs the same smart contract format, which is why the addresses look the same and why so many Ethereum applications also run on Polygon. Transactions settle on Polygon rather than on Ethereum, and the fee is paid in POL, the network's native token and the token staked to secure it.
A wallet that supports Polygon holds POL alongside supported Polygon tokens, including USDT and USDC, on a single address beginning with 0x. In a self-custody wallet the keys sit on your own device and nobody else can move the funds. In a custodial account, an exchange or a service holds the keys and you hold a claim on that company instead.
For the longer story, including where Polygon came from, the move from MATIC to POL and how the wider roadmap fits together, read What is Polygon? (POL). Moving between POL and local currency is covered separately, on buy POL and sell POL.
