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The guy at Home Depot told me that uncolored grout was the same as regular old mortar (not the thinset stuff). Since I don’t exactly trust the expertise at HD, I asked the people at the tile store. The tile store people said grout has different adhesion properties and should adhere better to the tiles’ edges and to itself, whereas the regular mortar was intended to hold stuff together. But they thought mortar might work as well as grout and to let them know if I tried it. They wondered if it would stand up to being washed as well as grout, but if you use mortar on exterior brick walls, I should think it would hold up to water, ice, etc.
The mortar certainly is cheaper!