In common usage it's pretty much interchangeable when you're talking about big mountains (or even small ones, I suppose). A number of difficult big mountains are technically a straight Class 2 walk-up, but I've never heard someone say they "hiked" Rainier or Kilimanjaro. Conversely, mountaineers who regularly tackle Class 4 & 5 stuff take understandable exception to people who walk up a peak and say "I climbed" so-and-so, when the real "climb" was on a steeper face.
Not being comfortable with anything over Class 3 (yet), which I would judge to be the true line of demarcation between the two terms, I try to avoid saying I "climbed" Whitney, Long's Peak, etc. - but I find that I do from time to time.
