Exchange
An exchange is an online service where you deposit currencies such as dollars or bitcoin (or any other crypto) and you can exchange it for some other currency for a small fee.
They require you to "prove your identity" and ask invasive personal questions in a similar way to opening a bank account.
Examples; Coinbase, Binanace, Kraken.
Broker
A broker provides an exchange-like service, but they do the actual exchange on your behalf for a bigger fee.
Wallet
A wallet is an app you install on your phone, or program that runs on your computer, or hardware device that allows you to store crypto currencies "in it". The reality is that the wallet stores your access to the crypto, and the crypto stays on it's network. Wallets allow you to send and recieve crypto and also execute smart contracts (explained later on this page)
Self custody wallet
This is a wallet where you actually store access to the crypto yourself and you have full and ultimate control over the crypto. You have to write down your secret words as a backup should you lose or break the wallet or the device running the wallet. Wallets will allow you to send and recieve funds to other wallets, exchanges and brokers.
Custodial Wallet
This is a service where a 3rd party such as a company holds the actual crypto for you and they allow you to have access to the crypto. You normally log in with an email and password to gain access. Exchanges act as custodial wallets when you send your funds to them or buy crypto with them.
Mining
Mining is the name given to the activity done by computers that run using electricity to secure the Bitcoin network and emit new Bitcoins. The energy used is converted to heat as the waste product. This is covered in detail in Bitcoin for Beginners Sessions 2 and 3.