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.
2 years ago was the first time to hunt elk and the first time to go into the mountains period. The Middle Fork broke me in very quick and humbled me too. We hauled our horses from Texas with no idea what we were getting into. The drive from Yellow Pine to Big Creek pulling a horse trailer was an eye opener. But, I fell in love with Idaho.