They usually join the RN and train as a sailor in their trade, usually a Medical Assistant in the Ratings/Other Rank world or as a Training Management Officer (commissioned), although there are a variety of other trades that can undergo All Arms Commando Course (AACC) at Lympstone to become an RN Commando (including Doctor & Padre!). Some elements of the Royal Engineers and Royal Artillery undergo the same course to become Army Commandos. All Commandos are employed within 3 Commando brigade. In fact 1Rifles (based in Chepstow) [Army] also act in support of 3 Cdo Brigade but are NOT Commando trained as a whole.
You will notice incidentally, the RN Commando Medic has a beard, (but cannot have a 'tache), the RM Commando Medic, trains as a Commando first, but can have a 'tache, not a beard. (In UK, or so the theory goes )
A Royal Navy Commando is a sailor from the RN who has passed the All Arms Commando Course. If you want to serve in 3 Commando Brigade then you have to pass the AACC. From the pics you gave it looks like the guy is a Medical Officer or Medical Assistent, serving within 3 CDO BGE. They wear the Green Beret but will have their former cap badge on it, not the Globe and Laural. RN CDO's would serve in the Medical branches in the Corps, Chaplincey and 148 Battery as FOO's.
This is the same for Army Commandos as well. They will then serve mostly/mainly in the artillery and engineer regiments attached to 3 CDO BGE. Hope this helps your questions mate, most of this is off the top of my head so I'm sure other posters will corect any mistakes!
The guy is an Army Commando:
Kept his old cap badge, will have the commando dagger like the two below and his flash will read "Army Commando"
Hope that helps! Might try and find another pic or two if your confused in any way!
Literally, non bootneck Commando trained ranks, have successfully completed the All Arms Commando Course. They are typically support groups and are an essential part of the Commando Organisation. The AACC is for trained military ranks only and is not open to new recruits into the armed forces.
Quite often, the training teams are shocked at the big difference in standards when some of these people start their AACC training. i.e. The big gap between the high level of training and personal standards produced by bootnecks and other militray personnel.
Typically: You have 59 Commando (Royal Engineers) and 29 Commando (Royal Artillery), you also have Logistics and REME personnel who are based at the Commando Logistics Regiment. Most matelots who do the course are usually medics and if I need to say it myself, all the ones I met during my service were excellent guys to work with.