Are there any specifics about how to differentiate a Pass and a Col in terms of mountaineering?
For non-mountaineering and non-geographical interests it's all the same.
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Both words refer to the same topography, which is a saddle point. The land goes up in two opposite directions, and down in the two other opposite directions.
To me at least, a col is just this basic topography. However, a pass implies the saddle point is a reasonable travel connection between the two downhill directions. Since the two uphill directions of the saddle point form a ridge, a pass is a point that allows reasonable passage over that ridge.
So a pass is a col, but not all cols are passes.
I personally think of it this way: Passes are less steeper, and are something which are/were used by people commuting for any reason for that matter. Whereas Cols are something which are comparatively steeper and there may or may not be an established walk-able path/trail through it.
Consequently, a Pass can definitely be approached from both the sides. Thats not always true/applicable to a Col.
Cols and passes serves the same purpose -- they are crossover from one valley into another. From geomorphological point of view, the Col is a saddle point between two peaks, whereas the pass is a saddle point between two valleys.
For example, Auden's Col is a saddle point between Gangotri III (6580 m) peak and Jogin I (6465 m) peak of the Garhwal Himalayas.