c-bert
Simplistically put, yes to your understanding. Yes FC do provide RC/RAS/RIS/FIS, but not in all areas within the UK. Also FC's do not in the UK provide Procedural service.
ATC will provide full services within their area, but will not control in other peoples airspace. An FC can control in the whole of the UK but clear of MATZ Zones and the London-Edinburgh/Glasgow spine. Their are other areas that FC's have to get clearance to operate in or require certain rules/events to be happening, but that is not for this forum.
FC's will take tactical aircraft and paint the picture so they can do the sortie, be it fighters or bombers. They also do AAR in certain areas that are their responsibilty and ATC does the other Mil AAR areas. All this whilst making sure that the Fast pointy things don't get in the way of the Passenger carrying jets. Certain areas in the UK can be booked to keep out the Passenger carrying jets but, they don'tr cover all the areas the Fast pointy things play in.
Your best bet is to go on visits to both sides. If your thinking of joining get it done through the careers office. But do do Airfield and Area for ATC and for FC do Boulmer, 1ACC and E3D's at Waddington.
Also do a search on the Mil Forum there quite a few threads re this very subject.
Trap One