I always heard the same, unbacked bows are the only "selfbows" as they are self backed. All other bows are backed bows.
Backings of any type: sinew, linen, silk, fiberglass, paper, rawhide, carbon, etc. serve the purpose of giving more strength to the bow that might otherwise break without these backings. In other words the backing is used to reduce the probability of limb failure.
In my opinion it is more difficult to build an unbacked bow as you are completely relying on one piece of wood. That is probably why some who actually complete this task are particular about what they are called.