I think you have over-simplified a bit. Lets see if I remember this...

These are AOS awards. Standards and definitions could vary with other organizations.

CBR (Certificate of Botanical Recognition) and CHM (Certificate of Horticultural Merit) give recognition to a specific individual plant meeting the requirements of the award. That plant and any divisions or clones may carry the award designation. Seedlings produced from the plant may not though they are often sold with the award to the parent noted. CBR is for a rare/unusual species with educational interest when that species has never gotten any award before. CHM is awarded to a species or natural hybrid plant for any aspect of particular horticultural merit.

AD (Award of Distinction) is awarded once to a cross, represented by one or more plants at the time, for a worthwhile new direction in breeding. It doesn't attach to any specific plant, and pertains only to that instance of the cross, not re-makes. Not for the plant, not for the breed, for the breeding.

AQ (Award of Quality) is awarded to a specific group of sibling plants exhibited together by one person, in recognition of the overall quality of the group, and including at least one plant that gets a quality award. It can be awarded to a species or a hybrid. Again, not for the plant(s) or the breed, for recognition of the quality of the breeding.

CCE and CCM are related awards at different point levels, given to the exhibitor not to the plant, in recognition of the high standard of cultural perfection attained. It wouldn't be awarded to an inferior plant though, no matter how well grown. It pertains only to that specific plant at that time. However, it usually happens that the award is noted for divisions and clones of the plant if they are distributed, or if the plant is used in breeding. It indicates that given good culture this plant can be a noteworthy specimen.