Many wallets can be installed directly to a desktop as a client.
This is the original way to generate a cryptocurrency wallet, using nothing more than a pen and paper to write down any private key generated.
This method has since been deemed unsafe and outdated. The risks associated with this method includes losing the paper key, or it being damaged or made illegible in some way.
Custody services are available for large sums of cryptocurrencies and are typically made available for institutional investors. As a certain level of wealth, crypto platforms will handle all aspects of storage for you.