Here is a picture to clearly show what "bearded" means in botany:
https://commons.m.wikimedia.or...
Firefox on my iPad wouldn't let me copy the image so that I could post the actual picture but at least this way you can see the creative commons blurb that is supposed to go with it
Note the plant's Latin name includes reference to the beard, Penstemon barbatus, since barbatus/barbate means beard, which in botany refers to having hairs.
Adding also to what Char said above, flower form divisions determined by AHS as the approved international cultivar registration authority are based on visual appearance, not their genetic background. I think there's some misconception "out there" that there has to be some kind of scientific basis for grouping flower forms for registration and exhibition purposes but there does not.
For a cultivar's registration (or patent) description to be universally understood and not cause confusion, it is necessary to avoid using long established and well-understood botanical terms for something clearly unrelated.