Commandos are generally troops who conduct quick raids behind enemy lines. The ones who are technically named Commandos are part of the British Royal Marines (who also wear Green Berets). They were formed during the early years of WWII at the urgings of Winston Churchill to raise morale and to scare the piss out of the Germans.
'Green Berets' are a nickname for the US Army Special Forces (there's a difference between Special Forces and Special Operations). Special Forces are trained for infiltration, recon, direct action (raids and the like), intel, and everything else a soldier can do (They are split up into 12-man A-teams at the lowest level. Commanded by a Captain, a Warrant Officer as XO and the rest are NCOs. Everyone has one primary specialty [weapons, intel, operations, engineer, medic] and everyone knows at least one foreign language fluently.). But on top of that, they also trained to infiltrate into the people of a country and raise and train a guerilla force which'll get help and supplies from the US (hence the requirement of a foreign language). Their main missions are recon and training, they are not often deployed for direct action missions (technically), that's the job of Delta (raids, snatches, counter-terrorism). Special Operations is any unit which is used for a special purpose (the scalpel rather than the sledgehammer) and is an all-encompassing term. Rangers, SEALs, Force Recon, you get the idea. Special Warfare is the term that the Navy uses for its SpecOps, Special Tactics for the Air Force.
As for unit designations, let's start from the basics of what makes a unit (Marines and Army infantry units). (Rough numbers based on the rule of three, give or take a couple)
Rifleman (Privates, PFCs, LCpls, SPCs, etc.)
3 Riflemen -> Fireteam (Commanded by a Cpl.)
3 Fireteams -> Squad (Commanded by a SGT in the Marines, SSGT in the Army) Designations go by 1st, 2nd, 3rd, etc. within the platoon.
3 Squads -> Platoon (Commanded by a 2nd Lt. with a SSGT [Marines]/SFC[Army] as a Platoon Sgt.) Designations go by 1st, 2nd, 3rd, etc. in the Company.
3 Platoons -> Company (Commanded by a Cpt., a 1st Lt. as XO, a Company Gunny in the Marines, a Company First Sergeant in both branches) Designations go by the phonetic alphabet (Alpha, Bravo, Charlie...) within the Battalion.
3 Companies -> Battalion (Commanded by a Lt. Col., a Major as XO, a SGT/MAJ [Marines]/CSM[Army] as senior enlistedman) Designations are either 1st, 2nd, etc. or if the unit has a history to it, it'll have it's own number (could be anything).
3 Battalions -> Regiment (Commanded by a Col., a Lt. Col. as XO, SGTMAJ/CSM as senior elisted) Designations are by the individual unit's number, and type. (Ex. 75th Rangers is the 75th Ranger Regiment, 1st Marines is the 1st Marine Regiment, 506th Infantry is the 506th Infantry Regiment and so on)
1 Regiment + support units ->Brigade (Same staff as a Reg., the Reg. is main unit), designations are 1st, 2nd, 3rd, etc. within a Division.
3 Regiments/Brigades (depending on the unit) -> Division (Maj. Gen. commanding, Brig. Gen. as XO, SGTMAJ/CSM as Senior NCO). At the moment, this is the primary manuver unit of today's Army (the current Chief of Staff of the Army is moving towards Brigade-style units). The designations are individual numbers (1st Infantry Division, 1st Marine Division, 82nd Airborne Division, etc.).
3 Divisions -> Corps (Lt. Gen. is CO, Maj. Gen. is XO, SGTMAJ/CSM is Senior NCO) Designations are with Roman numerals (XVIII Airborne Corps, I Corps, etc.)
3 Corps -> Army (General as CO, Lt. Gen. as XO, CSM (there are no Marine armies) as Senior NCO) Designations are by number (1st Army, 2nd Army, etc.) Not too many to go around nowadays, as today's Army is only 10 divisions big. Mostly just conduits of paperwork.
And the Marines have their own specially designated units too:
MEU (Marine Expeditionary Unit, one of the main Marine manuver units):
1 Infantry Battalion
1 Helicopter Squadron
1 MEU Service Support Group (logistics)
Commanded by a Colonel
MEB (Marine Expeditionary Brigade):
1 Infantry Regiment
1 Aircraft Group
1 MEB SSG
Commanded by a Maj/Brig Gen
MEF (Marine Expeditionary Force):
1 Infantry Division (reinforced)
1 Aircraft Wing
1 MEF SSG
Commanded by a Lt. Gen