Updated: May 20, 2019
Think of it this way the crypto wallet is your personal bank 🏦 *
1. Cold Wallets: This kind of cryptocurrency wallet uses keys created by a source that's not connected to the internet. This adds an extra layer of "air-gap" security and lets these wallets come in a hardware format. Usually some kind of portable Universal Serial Bus (USB) hard disk or thumb drive.
2. Hot Wallets: As you might expect, this kind of cryptocurrency wallet uses keys generated by internet-connected devices, typically servers at the wallet manufacturer's location or the wallet's back-end exchange. Even though the internet connectivity makes hot wallets notably less secure than cold wallets, they're still the most popular cryptocurrency wallets in use today since they're easily able to trade currencies, make internet purchases, and even access other kinds of digital assets besides cryptocurrency.
3. Decentralized Wallets: You'll see this term a lot, and it simply means that the cryptocurrency wallet has no centralized back end you need to work through when you want to sell, trade, or buy. You control your wallet's keys, and that lets you connect and generate a transaction with anyone, anywhere. Then again, you control your keys, which means you better protect the heck out of them or face a potentially very bad day.
4. Hosted Wallets: This is the opposite of decentralized, where the cryptocurrency wallet manufacturer or the exchange controls and stores your keys. On the one hand, they probably have better security than you do. But on the other hand, they're also likely storing thousands of users' keys, which means the hackers will be targeting them much more strongly than they would a single user like you. It also usually means that you'll need to begin your transaction with the hosted environment rather than simply connecting with anyone you like. That's not just an extra step; it also potentially impacts your privacy.
5. Paper Wallets: As the name implies, this type of cryptocurrency wallet boils down to printed sheets of paper that record your public and private crypto keys. To use a paper wallet, you simply transfer your digital currency to a public address that's shown on your paper wallet. To spend some of it, you simply initiate a transfer and reprint your wallet. Quick Response (QR) codes are often used to turn large chunks of typing into faster and less-easily-copied scanningoperations. Some folks don't consider paper wallets a separate kind of wallet, instead referring to them simply as the "coldest of cold wallets."
*credit to PCMag