This is my personal view on the topic. I don't claim it strictly matches any "official" definition.
A "hot" wallet is a type of wallet that's typically stored in internal storage of a network-connected device, such as your personal computer or your smartphone. This is riskier way of storing funds because they can be exfiltrated by malware. You would typically use a hot wallet for day to day transactions.
A "cold" wallet is a type of wallet where private keys to control the funds are never in contact with a network-connected device. They're typically stored in the form of recovery phrases written on paper or metal (in a secure location), or some kind of a smart card that securely stores private keys and exposes an interface to sign individual transactions (e.g. Ledger devices). Funds stored in a cold wallet are much harder to access, but are extremely (or completely) resistant to theft, short of physical access.
In crypto a "hot" wallet should be treated as cash, while a "cold" wallet is more like a savings account.
I don't know if it has a concrete definition but I generally say it to mean a crypto wallet that is directly or indirectly exposed to the internet.
It's possible to create a bitcoin wallet completely offline in a secure environment. The details to the wallet are then stored physically in a secure location/medium. This is called a cold wallet. People typically use a cold wallet for long-term storage of coins.
https://twitter.com/LukeDashjr/status/1609618498027753472
EDIT: Right, maybe it's all