No, trees do not grow back after stump grinding. No matter how the stump is removed, there will be no regrowth within a season or two. You may see very small sprouts and shoots near the ground line of the tree in one year and maybe some colored leaves in the spring (evidence of photosynthesis), but these are only after stump grinding, not stump removal.
Tree stump removal is the complete and total excavation of the stump or stump remnants from the soil in which it was growing. Tree stump grinding is different than tree stump removal. Tree stump grinding involves saw-cutting all the way around the stump inside a circular cutting guide, then excavating enough of the stump to remove it with an attached root ball. The round saw cut opening in this technique allows for better water drainage during rain events, but also provides space for numerous sprouts to grow out near ground level after stump grinding. These small shoots provide evidence that photosynthesis is occurring in one year post-grinding when they are about 6 inches tall (in zone 6), but more evidence can be seen by leaves on the stump in zone 6, where they are 12 inches tall in the spring. If you attempt to cut down a tree stump that is already present, a stump grinder might be attached to a stump grinder truck and used instead of an excavator. A stump grinder under this circumstance would reduce job time and save money by removing stump remnants more quickly.
Stump grinding is more convenient than stump removal because stump grinders can be used on standing trees of any size or age to speed up the process of tree stump removal. Stump grinding has been done for decades, but a major concern with stump grinder use in the past was that a stump grinder might damage underground utilities such as gas lines before they could be marked for protection. Today’s stump grinders have safety features which allow operators to avoid utility location markings so this risk is now low or even eliminated if utility companies mark their lines as required by law prior to any digging activity.