TL;DR
Hot wallets like MetaMask, Trust Wallet, Exodus Wallet, and Coinbase Wallet stay connected to the internet, making them fast and convenient for trading and everyday crypto use but more exposed to hacks.
Cold wallets like Ledger Hardware Wallet, Trezor Hardware Wallet, and KeepKey Hardware Wallet store crypto offline, offering much stronger security but less convenience for daily transactions.
Exchanges combine both: hot wallets for speed and withdrawals, cold wallets to securely store most user funds offline.