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Hot, Warm and Cold Wallets
The categories of wallets are really based on the security of your coins and if you hold the key or not.
In a hot wallet, also know as a custodial wallet, the company that created the wallet holds your Bitcoin. Some platforms only give you price exposure and don't neccessarly hold the asset, but simply make you a promise they will give you the amount gained in USD when you decide to exit your position. Some platforms do hold the actual asset and will allow you to move that asset to your own non-custodial wallet.
In a warm wallet, you have the keys so you are in full control of your Bitcoin. Warm wallets are those that are not on a device dedicated to storing your Bitcoin, such as a phone or computer.
In a cold wallet, you have the keys and you are using a dedicated device to store them on. Below is a list of cold wallet examples:
