A full node Stores a copy of the entire bitcoin Blockchain.
Prune nodes are also full nodes but they do not store the complete blockchain. You do not need to download the whole blockchain before you run a prime node. Although, it has some disadvantages to full node.
For example, you won't have to depend on exchanges or wallet to be able to verify transactions, you will be able to do that yourself as long as you have a copy of the block chain.
Who told you the exchanges are having full nodes. Exchanges wallet can be SPV if they choose it to be like that. Also, you can not run a full node on any exchange, unlike full clients wallet like Bitcoin Core.
In simple terms, a node is a computer that is running the bitcoin software.
Each individual computer is a bitcoin node
Your topic is too inaccurate and let's consider reason of making this thread while you don't understand about it but want to teach.
Not all 100% Bitcoin wallet softwares allow Bitcoin users to run a Bitcoin node.
Not each individual computer is a Bitcoin node. You only have a Bitcoin node if you run a Bitcoin wallet software that support a Bitcoin node.
He he referring to computers that are running full nodes. He is correct.