What is actually happening when I call JWT.verify - express

Question

I've came across two conflicting pieces of information and was wondering if someone could clarify what is happening. As far as I can tell jwt.sign is using a SHA algorithm to create a unique signature which, I saw on computerphile, is not a reversible process. On their video they explained that cryptographic signatures are not the same thing as encryption, as only encryption is a reversible process.
On that note, once I've created this unique signature and then enter it into jwt.verify as an argument, the code example at the bottom seems to reverse it like an encryption and assign the payload to a variable. So is this Bearer token/signature actually encryption? Also what part of the signature is used for verification, is the header and payload decrypted and ran through the signature process again to check it against the attached signature? Can someone please clarify this process because everything online is very wishy washy and or conflicting about the specifics of what is occurring.
function authenticateToken(req, res, next){
const authHeader = req.headers['authorization']
console.log(req.headers)
const token = authHeader && authHeader.split(' ')[1]
if(token == null) return res.sendStatus(401);
jwt.verify(token, process.env.ACCESS_TOKEN_SECRET, (err, user) => {
if(err) return res.sendStatus(403)
console.log('user ', user)
req.user = user;
next();
})
}

Answer 1

Okay so what i've not understood, is that only the last section of the JsonWebToken represents the hash signature. When the format of the token is as follows xxxx.yyyy.zzzz - where x is the header, y is the payload and z is signature - only z actually represents the SHA key.
When you've authorised the login, the signature is created, with the secret. Which is then checked during authentication, by using the base64 data in x and y. I thought the whole thing was SHA.