The term “hot wallet” describes a wallet connected to the internet.
The term “cold wallet” describes a wallet not connected to the internet (for example a hardware wallet unplugged and in a safe).
When cryptocurrency is in “cold storage” that means it is being held offline in a “cold wallet.” Funds you want to use like cash should be in hot wallets, funds you want to store long term are best held in “cold storage” in an offline wallet. Hot wallets are considered “hot targets” (i.e., they are targets for hackers). Thus, if you have a “hot wallet,” make sure you have as many layers of protection on it as you can (two factor, strong password, all security settings on, etc).
Keywords: wallet, hot, cold, funds, store