High altitude trekking in mountains is even better than long distance running, at least in terms of breathing and sweating.)
The crucial difference is in variety of breathing patterns on a trail - it changes with a terrain, in contrast to steady breath while running on a flat surface.
I do both - moderate distance running (10-15km) and up to 6000m trekking as a guide.
there is no clear definition, but for most mountaineering starts when you need technical equipment (crampons, ice axe etc). I do hikes in alps in non-winter almost every weekend in 2000m-3000m band and its pure hiking.
There are peaks higher than 6000m where you will not need this (ie in andes, tibet), and there are much lower peaks where you can't do anything without it.
One example I did - you can do Kilimanjaro without touching any snow or ice, via standard route, and that's 5895m high.
I've always gone with the concept that mountaineering starts where a rope is needed to prevent serious injury in case of a fall. Altitude or even protection is outside of the equation. A sidewalk, if beside a 100-foot drop, counts as mountaineering because the rope is needed.
The crucial difference is in variety of breathing patterns on a trail - it changes with a terrain, in contrast to steady breath while running on a flat surface.
I do both - moderate distance running (10-15km) and up to 6000m trekking as a guide.
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