These two words sound the same but have very different meanings.
Shear has many uses related to cutting or separating—the kind of cutting done with scissors, not with a knife.
Sheer is mainly an adjective meaning absolute or pure, but it has other meanings,such as steep and diaphanous (more explanation below).
That’s a brief overview, but much more can be said about these two words.
Shear can be a verb meaning to cut—especially, to cut off the hair of sheep, or to cut human hair in a similar way (to cut it all off). As a noun, a pair of shears (plural) refers to large scissors. You can say shear (singular) for one blade in a pair of shears.
As a verb, to shear can also be used for the cutting of tall grass, using a sickle (a long curved blade), and for another very specific kind of movement—the sliding movement of solid things coming apart, separating from each other:
During the earthquake the side of the mountain just sheared off.
Shear also describes when one member of a group of moving things separates from the group, heading away at a slight angle (like a sliding cut):
One plane sheared off from the group to investigate the call for help.
Shear can also be used to mean take away:
The refugees had been shorn of their hopes for peace.
Finally, shearing describes any force which causes things to slide apart:
Earthquakes are often caused by a shearing force between tectonic plates.
Sheer, on the other hand, is an adjective, with a variety of meanings:
Sheer meaning absolute or pure:
Conspiracy theories are usually sheer nonsense, with no factual truth!
Sheer meaning steep:
Climbing a sheer rock-face is scary and requires good equipment.
Sheer meaning diaphanous—thin and partly transparent (see-through), for clothing, or anything soft, such as a curtain of water:
The sheer material of her dress was almost transparent.
Sheer can also be used as an adverb for steeply or for absolutely, purely:
The trail ran sheer up the mountainside. (steeply)
Finally, some people use sheer as a verb meaning to change direction—which may come from confusing sheer with shear, but it is acceptable.