A "clearance" is a somewhat more formal contract with ATC. When used in it's purest sense (as in the US system) it promises some level of separation in return for agreeing to fly a specified trajectory. I would concede that in UK usage for class D, it has become little more than a "permission".
Rather debatable.
European definition...
Air Traffic Control Clearance - Authorisation for an aircraft to proceed under conditions specified by an air traffic control unit.
= an ATC unit granting permission to operate in an ATZ is passing a clearance.
2 s