@DavidR
When we classify things we often use a hierarchical approach. As an example we could have a top classification of objects that floated on water as "ships". So a passenger liner would be a ship; an oil tanker would be a ship; a battle cruiser would be a ship; an aircraft carrier would be a ship. They are all classified as ships but they are not the same. They share some characteristics but do not share all of them. We could have sub-classifications within ships for different types of ships so for example, different types of cargo ships.
The daylilies that are derived from Bee's Bettie Sue [BBS] (and other cultivars) can be classified as having a type of crest. Their crests may be larger horizontally than vertically. Other daylilies can also be classified as having a type of crest. In their cases the crests may be larger vertically than they are horizontally. Some daylilies may have crests that originate in one location and other daylilies may have crests that originate in different locations.
Many different combinations and permutations of the characteristics associated with unusual growths on the petals and sepals could be classified as crests. Within that classification there could be sub-classes that separated groups of cultivars that shared certain characteristics.
The daylilies that are derived from BBS cannot be correctly botanically classified as having beards. To be classified botanically and scientifically correctly they would have to consistently have hair, or hair-like structures that are accepted botanically. The plant species, bearded aloe, bearded grasses, etc., have common names that include bearded based on their consistently having structures that are considered botanically as hair-like. A plant may have many different common names - they are not required to be scientifically correct. The daylilies derived from BBS do not have structures that are considered botanically correctly as hair-like.
The classifications of daylily types by the AHS are not designed for hybridizing. As an example, doubles are not all identical - there are different types of doubles. Some doubles are hose-in-hose, some are peony type and some are both but they are all combined under the double classification.