However... I have been "caving" many times, over many years.
As far as I can determine the word "spelunking" was coined by two American cavers in the 1930s, to sound clever. The root if I can remember the correct spelling, is Spaeleos, Greek for "cave", but where they found that strange "unk" syllable is anyone's guess.
The word never caught on outside of the USA, and although journalists tended to keep using it to seem clever, American cavers themselves eventually relegated it to denigrating novices (they'd never been beginners themselves, of course) and dilettantes. I have never seen it in any American cavers' literature.
"Speleo" appears in the umbrella term for the science of caves and their contents: Speleology (again that should have the "ae" but I forget which side of the first 'l'). So the professional or amateur cave-researcher is a "speleologist" - but the words are not used to describe "just" caving and cavers. In fact many of them simply use the ordinary words, "cave-science / cave-scientist".
.
To answer ZAK.....
"... when things go wrong."
Well, were the films genuine documentaries of real caving incidents? Or were they fantasies invented purely as entertainment by people who know nowt about their subjects....?
Things can and do go wrong, and I have assisted on or or two rescues, but they do so rarely and of them, fatalities are thankfully rarer still. Though one of the oddest caving accidents I read of, was of a caver somewhere in the USA injured in a cave's vertical entrance shaft by a racoon falling on him!
Caving is not a so-called "extreme sport" (gratuitous stunts), but is like any other non-competitive outdoor-pursuit: you learn to understand the natural hazards, and the techniques and equipment, so although the caves' intrinsic hazards remain you greatly reduce the risk of an accident from them.
Of the cave-rescue incident reports around the UK - if those of the USA are comparable it may depend there much more on the geography of each caving region - most of the call-outs are not to lost, hurt or trapped cavers, but to hill-walkers and farm animals on the surface! Occasionally, to assist Missing Person searches not related directly to caving or hill-walking ; very occasionally, to help tourists taken ill during a show-cave tour.
Of the underground incidents, I think most are "Lost / Overdue" calls. Injury rescues are fairly unusual; though I have known two or three cavers badly injured in various ways.