“Commandos”, strictly speaking, refers to the forces that were set up and run by Combined Operations Headquarters, commanded by Louis Mountbatten. They were (I believe) an inter-service group, and they were specifically set up to conduct raids on Occupied Europe. They weren’t the same as the British Paras or the SAS or the Royal Marines, which were all specialized units within either the British Army or the British Navy. The main connection between the Commandos, the Paras, the SAS and (over on the American side) the 82nd and 101st Airborne and the Army Rangers is that all of them were elite units of one sort or another: highly trained, able (and often expected) to function in small groups or on their own behind enemy lines, and often skilled in close-combat techniques. The Royal Marines don’t necessarily fit that pattern, in the sense that their primary mission wasn’t to conduct raids or to conduct parachute drops or to take specialized objectives like Pointe du Hoc (which was a Ranger target on D-Day).
To give a US parallel, the USMC created two raider-type batallions during WWII which were much more Commando-like in training and function than the Marines in general. The USMC was (and is) highly skilled in conducting amphibious landings against very tough targets, but if you compare Iwo Jima against the raid on Makin Island by Carlson’s Raiders (the 2nd Marine Raider Battalion), you’ll see that Iwo Jima was a large scale take-and-hold invasion while Makin was a small-scale hit-and-run raid.
But it’s true that elite forces in general have a disproportionate affectation for berets. It’s a romantic soft spot among these otherwise very tough guys.