Three main types of wallets include hardware wallets, software wallets, and web wallets. Hardware wallets store your personal keys in a physical object that looks something like a USB stick. This wallet is a form of cold storage, and is therefore the most secure.
Software and web wallets are both hot storage and can be accessed through the internet at any time. Software wallets include any sort of phone app or software application on your desktop that can be used for storing crypto private keys. Web wallets are similar, but they can be accessed through a web browser instead of an application.