MC = master (or mistress) of ceremonies.
DJ = disc jockey.
Some DJs are also MCs. Like Dr. Dre, who started on turntables and later moved into MCing. In fact, it seems most hip-hip artists (at least older West Coast guys) do a little of both. It should be noted, though, that to DJ, you need turntables, a mixer, a PA, records… stuff that isn’t cheap and easy to come by. MCs can just grab a mike and do their thing.
Some MCs, as far as I can tell, aren’t anywhere around the turntables but still go by DJ. Like DJ Quik.
Don’t know about electronica, so hopefully someone can help you there.
A club DJ, depending on the gig, might just be up there spinning records. The DJ of a rap act has a somewhat different job; he helps create the act’s songs by gathering samples from older music and mixing the hooks together. Of course, experienced club DJ’s do this too. But the club DJ’s job is to keep you dancing using records at hand, while a DJ as part of a hip-hop act’s job is to create music with his MC(s).
And it all started in the late '70s and early '80s when clubs would host big parties with DJs, and MCs would go out in the streets and advertise the parties by rapping. They’d rap about their DJ being the best around, and dis the competition (other DJs and MCs) – that’s how competitive rapping began.