Grout is the colored compound that is mixed up and placed between man-made and natural stone tiles to bind the installation in place and add an extra element in terms of design. While grout does have concrete as parts of its ingredients, it is not an adhesive and cannot be used as such despite its similarities to thinset mortar.
Thinset Mortar Basics
Thinset mortar is the adhesive that most tile installations are installed with. It is a combination of cement, sand, polymers and lime that are mixed with water to create a creamy mixture that sticks to tile as well as the substrate the tiles are adhering to. It does have colored additives and while it can be used as a grout in special circumstances, it is the preferred mortar for installing tile.
Grout is similar to thinset mortar in most ways. It contains cement and polymers, as well as sand, but it has a tiny amount of lime in comparison, just enough to add only a slight stickiness to the grout. As a result, it lacks the stickiness of mortars and is not an acceptable mortar compound. Grouts also contain colored additives that are meant to tie in an installation visually and add aesthetic appeal, while the cement helps hold the grout in place and form a grid pattern of cement lines that add stability to the installation.
Another major difference between mortars and grouts is the amount of water that is added to the mixture. Thinset mortar is mixed to the point where it is creamy, like peanut butter, so it can be spread on with a notched trowel but also have enough thickness to withstand the weight of the tile. Grout, on the other hand, has more water added to it and is a creamier mixture that is pushed into the joints with a float or grout bag. The ratio of water to grout makes it impossible to use as a mortar.
The most important difference between grout and thinset mortar is the addition of polymers. While grout does have latex and a small portion of lime to add to the elasticity and stickiness of the mixture, grout lacks the polymers that are specifically included in thinset mortars to create the adhesive effect that holds tiles in place. The only thing that would happen if you tried to use grout as a mortar would be the back of the tile getting slightly dirty from the grout because there are no adhesive polymers to bind the tile.