Cultivar: My understanding of the International Code of Nomenclature for Cultivated Plants (ICNCP, Cultivated Plant Code) is that there can be only one cultivar of a given plant. The registered cultivar name takes precedence to any other. Older plants (pre-the digital age) may have several cultivar names but the oldest takes precedence.
Trade Name: Given by the plant breeder, not in any way affiliated or controlled by the Cultivated Plant Code
Synonym: Basionyms, Invalid, Illegitimate, Unplaced, Synonyms - listed in The Plant List.org, ITIS or TROPICOS
Common Name: A non-scientific name that one or more people have chosen to give to a plant
There appears to be a gap. I threw Alocasia x amazonica 'Polly' in common names - it shouldn't be there. But it shouldn't be in the synonym list either and it certainly doesn't belong as a separate plant. Nor is it a cultivar (the correct name 'Poly' can be traced back to a breeder and date).
What I propose is a new field "Also Sold As" directly under Trade Name that would allow multiple entries for the various wild and whacky names under which a plant might be sold. It would need to be searchable.
Using Evan's Leucanthemum x superbum 'Leukal 01'; the Trade Name is Goldrausch, Also Sold As: Leucanthemum x superbum Gold Rush, Leucanthemum x superbum Goldrush, Leucanthemum maximum Goldrausch; Common Name: Shasta Daisy; Synonyms: Leucanthemum superbum, Chryanthemum... etc.
Just a proposal to ponder...
