Most MUAs will be expected to be proficent in both, and should have been trained in boh, and many will start out as haidressers. Only in very high budget films will you have sepearte departments. However, you will find that most mua's will perfer one over the other.
I do both, I think you can really perfect an image when you can do both. I find I get booked for both on most jobs because its easier for a client to book someone that can do both, of course I am better at make up than I am hair but you get better as you go along, practise makes near on perfect! lol
when I was doing my VTCT Diploma I was told that it is generally expected for a make up artist to do both to be able to acheive the full look and work your way up to those great jobs, what someone said earlier about on a large production, you will be one or the other, thats because there is plenty of cash to splash around. as well as being traind in hairstyling cutting and colouring on my make up artist course, i have an extra NVQ hairdressing to home my skills and be able to offer mobile hairdressing services to my list.
So I guess the more skills you have the more you have to offer a potential client