What’s the difference between an ordinary drill and a Dremel-style rotary tool?

Alan Chenkin, Trained as a Machinist/Mechanic in the NYC schools, Life long Mr. Fixit

The Dremel is better suited to craft or fine work, and is adaptable (with a multitude of bits and adapters) to hobbies, craft work, engraving, and more.  Power drills are typically larger, more powerful, and turn at a slower RPM with more torque than a Dremel rotary tool.
When I am on the job, I carry several drills, and keep my Dremel (and all its bits, polishing wheels, and cutters) at the shop. That is because I am usually working on larger projects that are not suited for a small Dremel tool.
Here is a huge set of Dremel accessories:
I don’t use my dremel a lot, but it is a unique and useful tool for polishing, work on small metal parts, drilling tiny holes, making jewelry, and fixing keepsake boxes and the like.  They key to a Dremel’s usefulness is the sheer number of bits and accessories you can get.  Look at the selection on EBay.
Have fun, and Dremel on!