The maroon beret means that they have completed the para training course (P-company and parachute training) but the still belong to RE (a branch of Service). The one wear the Parachute Regiment cap badge are members of the Parachute Regiment. RE, Signal, RAOC etc are NOT regiments they are corps.
In the british army there are two type of soldiers, one is we call teeth arm, such as parachute regiment, guards, armour etc. the other are call service arm such as RAMC, signal, RE etc.,
Regards
Kenneth