Hot, Warm and Cold Wallets
The categories of wallets are 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. These platforms 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. Examples of platforms that will allow you to move your Bitcoin are Gemini, Kraken, Swan Bitcoin and Cashapp. Examples of platforms that only give you price exposure are WeBull, RobbinHood and SoFi.
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 for storing your Bitcoin, such as a phone or computer. Being on a device that is exposed to the internet and a lot of other applications makes the wallet less secure, not by the nature of the wallet software itself, but by the nature of the device the wallet is on.
In a cold wallet, you have the keys and you are using a dedicated device to store them on. Having a dedicated device makes it easier for the developer to secure the device as the attack surface for the device is very small. There are many to choose from but, below is a list of cold wallet examples:
