What kinds of wallets are there? Can I get short a explanation about cryptocurrency cold/hot wallets?

Are there more kinds?
Hot and cold in this case refer to if the private key is stored on a system connected to the internet or not. Hot wallets are stored on system connected directly to the internet. This can be on the client machine or on a centralized server. A cold wallet can be a HW wallet, an offline wallet or a paper wallet. You kind of create an air-gap that drastically reduce the attack surface on the wallet.