There are two topics going on in this thread:
1) Should we change the way the names are displayed? That discussion is ongoing and really we should be discussing it in the Plants Database forum rather than Site Talk.
2) Why does the search display a different order than the various browsing tools? Specifically, why is the search not alphabetically ordered?
The answer to #2 is simple: search is different than browsing. Browsing is where you are given a list and you click through the list and view it. The list was prepared ahead of time and is tightly confined to exactly what is in the list. For example, "View all plants in the genus Solanum" is a list that was prepared ahead of time and the contents are shown alphabetically.
Now, when you do a
search you are typing in whatever you want, and the system then digs into its database and tried to find what matches what you typed in. Then, it finds everything that matches and tries its best to give it to you NOT in alphabetical order, but rather in the order of what it thought is closest to what you searched for.
A non-ATP example here is dmoz.org, which is a website directory. You can search it for airplanes:
http://www.dmoz.org/search?q=a...
Note that it lists a bunch of websites, and they are not alphabetical. They are in some other order that is determined by their internal software. That is how searches always work.
But you can also browse their lists. Click on one of their categories up top, for example, this one:
http://www.dmoz.org/Shopping/R...
And now you see them all in alphabetical order. That's because you're now no longer search, but browsing a pre-prepared list.
I hope this explanation helps you understand the different between searching and browsing, and why we display things the way we do here at ATP.