Correct term: acclimate v. acclimatize (adjusting to higher elevations)

In my ongoing IMHO thread on the challenges of hiking/climbing 14,000 ft. peaks in Colorado, I wasn’t sure which word was correct.

In his book, Jon Krakauer used acclimatize, though I’ve heard some use the term acclimate. Which is correct and is their any difference in meanings?

OED Online says they’re synonymous.