Joanne, a variety name is not a botanical term in the sense often used. It's less confusing to use the term variety only for botanical varietas such as Aquilegia flabellata var. pumila and Aquilegia flabellata var. pumila 'Silver Edge'.
Fan Columbine (Aquilegia japonica)
Fan Columbine (Aquilegia japonica 'Silver Edge')
Trade names are not varieties in that strict sense.
Patents note a registered cultivar name.
Cultivars must be registered and accepted.
Cultivar names cannot be trademarked.
Trade names are applied to a registered cultivar to allow the owner to market the plant in a proprietary way. A patent will expire while a trademarked Trade name can be renewed indefinitely.
