As a mountaineer and a climber I would call a spire a "spire", or a "tower". A cliff of moderate size, 50'-400', with no defined summit is a crag. Cliffs larger than that are called "walls", or "big walls". Many of the cliffs on the hike up to the Grand Teton are called crags in the climbing guide. Only the actual mountains have proper names, or some of the spires attached to the peaks. The rock outcroppings at City of Rocks in Idaho would all be called crags. This is a spire.
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