Hi, David. This is not stucco, probably, just textured plaster. Some people prefer the look to smooth plaster walls and it kind of goes in and out of fashion and is more popular in some parts of the country than others.
The best way to get this smooth is to sand it. You use a sanding screen on a sanding block and these are available at home centers with poles that mount to the block so you can work from the floor and not from a ladder. The sanding screens can be pretty coarse, but they come in several grits. Start with the coarsest one you can get and finish with fine when you get the ceiling flat and the old paint off. This really is not too bad a job but will be very dusty so wear a good dust mask and full coverage eye protection. Good luck. Henry in MI