Wallet 

A (crypto) wallet is comparable to an online bank account. These wallets are both a gateway to access blockchain and an interface that lets users store, send and receive cryptocurrencies. There are three popular categories of wallets: (non)-custodial, hot, and cold wallets. 

Non-Custodial / Custodial Wallet

A non-custodial wallet is a decentralised type-of-wallet, where the user owns its private keys. Having the private keys allows you to have full control of your tokens or funds. The risk, however, is that if you lose your private keys, you will also lose all your funds. Contrary to non-custodial wallets, custodial wallets (e.g. a third party) hold funds on behalf of their clients. This means that the funds are not tied to a blockchain address under your control. Instead the wallet provider is responsible for securing them. The advantage is that you will not lose your money if you lose your private keys!

There are several types of non-custodial wallets, namely web wallets, hardware wallets, Mobile Light wallets, desktop wallets, and paper wallets. 

Hot Wallets 

Hot wallets are tools to store your cryptocurrencies and are always connected to the Internet. The stored tokens or currencies can be instantly exchanged with other members of the network or used to trade. Hot wallets are meant for frequent use, they can come in the form of an application (a desktop wallet), on a phone (a mobile wallet) or be hosted by a third party (a web wallet).

Cold Storage / Cold Wallets  

In contrast to hot storage, which are typically online to allow for fast deposit/withdrawal, cold storage refers to offline storage of cryptocurrencies or tokens through the use of hardware non-custodial wallets, offline computers or paper wallets.

Cold wallets can only be connected to the internet through physical effort (e.g. plugging in the USB, turning on a hardware wallet). This provides an extra layer of security compared to wallets that are stored on devices connected to the internet (e.g. phone wallets). Cold wallets are intended for secure and long-term storage.