I always like to think of body as the feel of the smoke such as if the smoke has a heaviness in the mouth or maybe it leaves an oiliness over the palate. Some smoke I find to be really light and "fluffy" so to speak, or leaving the palate feeling dry. Strength I think of the power of the smoke such as the difference between a Fonseca and Opus Power Ranger. Then there's the spice that I think of as the peppery feeling that hits the back of the tongue and throat, which can range from none to eye watering black pepper.
Mild, medium, and full can be used for all of these, such as a full body (heavy) or mild body (light), mild strength (Fonseca) or full strength (Opus), and spice having mild strength (barely any), medium (white pepper), or full strength (strong black pepper).
I try to think of the flavor of a cigar separate from mild, medium, or full. I use the word rich and bland with flavor and then discern specific tastes that I pick up.
Again, just my thoughts on it.