SE is Special Equipment, the British designation. M is the same package in North America. MC is the American car with the C-type cylinder head as well.
You will find it asserted — by dealers, by buying guides, and across the internet — that MC stands for "Mechanically Complete", or for "Means Competitive". Both are wrong, and the chassis prefixes show why. A denotes Special Equipment with the standard head. S denotes Special Equipment with the C-type head. M existed on its own, for the package without the special head. MC is simply M plus C.
What the Special Equipment package contained
Wire wheels, twin fog lamps, a dual exhaust system and a high-lift camshaft profile, with the C-type head available on top as a separate step.
The C-type cylinder head
The head developed for the C-type racing car, with modified porting. With it, and a revised ignition curve and the dual exhaust, Jaguar claimed 210 bhp at 5,750 rpm against the standard car's 190 at 5,500.
One commonly repeated claim deserves care. Special Equipment and C-type cars are widely said to have run 9:1 compression. A genuine MC drophead sold at auction carries engine number G8354-8S — C-type head, and an 8 suffix. Whatever the truth about the option list, 9:1 was certainly not universal on C-type cars.