Yo male it easier for one to understand, crypto wallets are classified into three;

1. Medium; What type of medium is stored on?

2. Connectivity; Is the wallet connected to the internet?

3. Custodianship: Who has access to, and therefore,  control of the wallet's private keys?

1. Crypto wallets based on Medium.

In terms of Medium, wallets can be broken into 4 main Categories;

a) Software wallets;

Software wallet is a computer program or mobile app that holds private keys online. They connect crypto networks through trusted full nodes, centralized services eg. Centralised exchanges, or full nodes themselves. 

Software wallets includes; Desktop wallets that are used on a desktop or a laptop computer, Mobile wallets that work as a mobile app and are used on smartphones,  and Web-based wallets that work as a browser extension and are used in web browsers. 

b) Hardware wallets;

Hardware wallet is a small, portable physical device that keeps private keys isolated from tje internet at all times.

To transact, a computer and the device manufacturer's software application are required to authorize the transaction since the private keys are kept offline.

Hardware wallets provide extra layer of security than software wallets but most people don't use them since they are complicated and the devices themselves are expensive. 

c) Paper wallets;

A paper wallet is literally a piece of paper with your address and private key printed or written on it. 

Paper wallets are created by downloading software, then running the software offline to generate a public/private key pair which you print out on a piece of paper.

d) Brain wallets;

A brain wallets is a private key that is stored in the user's memory  in the form of a seed phrase, which is a sequence of 12 - 24 words. Also known as Mnemonic phrase. 

They're similar to paper wallets only that nothing is printed or written down on a paper but stored or mastered in the brain.

If you ever forgotten a password,  ca brain wallets is definitely not for you. 

2. Crypto Wallets based on Internet Connectivity. 

We have two categories here;

a) Hot wallets;

The "hot" in hot wallets refers to its connection to the interwebz.

A wallet is considered hot when;

• The wallet can be directly accessed through the internet or,
• The wallet is on a device that is always connected to the internet. 

Advantages of Hot wallets

• You can access it from anywhere with an internet connection 
• It's easier to recover access if you lose private key than cold wallets.

Disadvantages of Hot wallets 

• Your keys are kept on the third party's servers.
• Vulnerable to a wider variety of attacks than cold wallets making it less secure.

b) Cold wallets

The "cold" in cold wallets means the lack of connection to the internet.

Because cold wallets are never connected to the internet, online theft of your crypto assets is almost impossible. A hacker would have to physically steal the device to gain access to your crypto assets.

3. Crypto Wallets based on Custody.

When it comes to cas, there are two ways to keep it safe;

• Do it yourself and assume full responsibility.  
• Trust someone to do it for you. Like a bank.

With Cryptocurrency,  custody refers to the ability of a trusted entity or a third party to hold and protect its customer's private keys and Cryptocurrency holdings.

In terms of cryptocurrency,  crypto wallets can be broken into two categories;

a) Custodial wallets; 

The wallet provider has access to your crypto assets. The assets are controlled by a trusted entity, with the user typically having to access its contents via a web interface. These sites store private keys for you hence no worry about them.

Custodial wallets are also known as hosted wallets. Wallet is considered hosted because a third party holds for you, similar to how a bank holds your money in a savings or chexking account.

b) Non-Custodial Wallets; 

This gives the user full control of their funds and the associated private keys or seed phrase. This sounds great but that also means that YOU are the solely responsible for the security of your own private keys.

With non-custodial wallets provide the software necessary to manage your crypto assets, the responsibility of keeping your privaye keys safe falls entirely on YOU. There is no third party or a custodian to keep your crypto safe.

If you lose or forget your private keybor seed phrase, there's no way to access your crypto assets. They are stored on any online server by a trusted third party and are therefore much less susceptible to theft or hacking.

If you lose them, you losebyour finds for ever.