Can message signing be used to let a user sign a transaction?

Today I want to try Polygon and realized that I am required to sign a message to get in. Paranoid by all the scams I'm reading about I wanted to figure out what the message is. I didn't really find a real answer yet. Is it exactly the message metamask shows me?

I used remix to generate a small hashfunction and when enter the text from metamask in there it doesn't return the same hash I'm seeing on my ledger.

pragma solidity ^0.7; contract VerifySignature { // use this function to get the hash of any string function getHash(string memory str) public pure returns (bytes32) { return keccak256(abi.encodePacked(str)); } } 

My main issue is this: Wouldn't it be possible that polygon gives me a transaction of ethereum from my wallet to someone elses, I sign it and then my money can be withdrawn? I hope this isn't possible and I'm pretty sure it isn't but I don't understand why.