Dolls use bases. Some "dollers" do make what we call baseless dolls. As long as you are making it with the intention of being doll and placing it into the proper category then it qualifies. Human, or mostly human (anthro/fantasy etc). Also for the most part dolls focus on design especially clothing and hair.
In my eyes, it's like regular dress up dolls and action figure dolls. Some come in one piece (like plastic) and some you put the clothes on but they are very much alike. Dolling has been around on the internet for a very long time. People started making them for website customization and collecting them and sharing. They stemmed from very strange looking pixels and turned into digital doll makers and avatar websites like the doll palace.
If you think of digital doll makers, dollers are people who use bases and make their own clothing, bases, hair, everything.
You asked a very good question by the way.
Also I must mention the "dolling" community we have many branches from the same roots and it can mean different things to different artist.
This group is what I would consider traditional in it's approach and like all my groups I do not support use of "traced" bases made from images without permission or being original work.
Thanks for asking this!