There are actually quite a few differences between mortar and concrete. When you think of cement, you think of those big trucks that keep turning the body. Now if you think of cement as a binder, similar to a recipe with flour, the cement is the flour. The purpose of cement is to hold other materials together. But, you can't use cement alone, you have to use other materials mixed into the cement, such as limestone, calcium, silica, iron, aluminum, among other ingredients. This mixture is heated in a real large kiln to 2700 degrees. This produces clinkers, a solid material like solid pieces of stone. This is then ground down and mixed with more materials such as gypsum to create the gray concrete substance. That gray substance is then added to water to make foundations and sidewalks and other things that need strength.
Mortar is used to hold building materials together, such as bricks and stone. Think of mortar as glue. Mortar is made out of water, sand, and some of the cement material we talked about above. You mix it with water to get to the strength you want and it is then used to hold building materials together. There is an age to mortar. If you go into some old houses with stone foundations, you'll see powdering of the mortar. That's just a function of age. We can take that old mortar out and put new mortar in to maintain the structural integrity. To sum it up, mortar is the glue that holds materials together.