We do strive for consistency, and if you find examples of inconsistency, please bring them to our attention. We use the trademarked name for alphabetization if there is a trademarked name. Otherwise, the entry is alphabetized under the cultivar name. Other names are also present in the entry as "also-sold-as" names or alternative cultivar names, but they aren't alphabetized under those names in the alphabetized listings. 'Herbstfreude' was a well-established name long before the name 'Autumn Joy' was invented for the English-speaking market, and even in the English-speaking market the plant is still sold as 'Herbstfreude' by some vendors. 'Autumn Joy' is included in the 'Herbstfreude' entry as an also-sold-as name, so it is included in search results.
Your use of the term "botanical name" is misleading, Deb. The botanical name is the Latin name of the plant. In your example, it's Acer rubrum. It does not include trade names or cultivar names.
The "cultivar name" can be a denomination code the hybridizer uses for registration and patenting, sometimes before the plant is given a marketing name. It can often be unpronounceable and immemorable, and I suspect that it isn't even remembered by the high-volume hybridizer after a more memorable name is chosen, so it wouldn't make much sense to alphabetize our plants under those codes.