"Crest" is used to describe the high point of a wave, whereas "peak" is used to describe the high point of a mountain. "Peak" can also be used to describe the point when something is at maximum intensity or development (i.e. "He reached his physical peak in his early twenties", "Sales usually peak during seasonal holidays").

I agree. It's very rare to hear the word 'crest' used to refer to anything other than a wave, whereas 'peak' is a very common term - used literally for mountains and figuratively in sport, business and many other contexts.

The short answer is, yes: a wave has a "crest," a mountain has a "peak." But of course it's more complicated than that. The phrases "mountain crest" and "crest of the mountain" are actually perfectly valid and common. "About this time a small squad of men reached the top of Lookout and planted the Stars and Stripes on its very crest."--General Sheridan. "...over the crest of the range to the border of the Mojave Desert at an elevation of 3500 feet on the north" "Mammals of the San Gabriel Mountains." In the context of mountains, a "crest" means specifically a ridge, a long _row_ of high territory (e.g. a "sierra" in Spanish or indeed--I think--"cresta" in Italian or "crête" in French. A "peak" suggests a single isolated summit, like that of the Matterhorn. And a "wave" can have "peaks." In electronic engineering, it is customary to refer to the "peak-to-peak" voltage of a "wave." That means the distance between the trough and the crest, but nevertheless that is the phrase.