Supercells often develop rotating winds inside them known as mesocyclones, associated with strong tornadoes. However, scientists don't yet understand the connections between mesocyclones and tornadoes that actually reach from them down to the ground. Not all tornadoes come from supercells, but the strongest twisters usually have a supercell as a their parent. Weaker vortices, such as waterspouts like those common in the Florida Keys, can come from cumulus congestus clouds, also known as towering cumulus. These are tall, thick cumulus clouds that might be producing rain but not thunder and lightning.
Some researchers use the term landspouts for similar twisters that form over land instead of water.
Gustnadoes are weak vortices that are not connected to the cloud base, and by definition are not tornadoes. They are relatively shallow vortices associated with intense, small-scale shear in a thunderstorm gust front. It can take a very alert and experienced spotter to tell the difference.