DDOS is more different than that. Imagine DDOS protection as a gatekeeper, server as an autopark while requests as a car going into it per seconds
A gate keeper typically accepts traffic in a regular rate. However, hackers who have managed to steal millions of cars at a time, decide to make them all push forward to the autopark for the purpose of distrupting it.
If the gatekeeper doesn’t control the incoming traffic, it will all rush onto the autopark which will cause the autopark to be crammed as fuck. Unlike cheat software which could be visualised as something built inside one of these cars and searching them without violating privacy is kinda tough, you can do whatever upgrades needed to your gatekeeper to block the millions of rushing cars.