A crypto wallet doesn't store your coins the way a physical wallet stores cash. Your cryptoassets exist as entries on the blockchain itself; what a wallet actually holds is the private key that proves you control a particular address and lets you sign (authorise) transactions from it.
Wallets are broadly split into "hot" wallets (connected to the internet, convenient but more exposed) and "cold" wallets (kept offline, usually on a dedicated hardware device, far more resistant to remote attacks). Which you use — and for how much — is one of the most important practical security decisions a new crypto user makes.