Susan, Richter's separates the basils into groups: Sweet, Genovese, Bush, Purple, and Other.
Johnny's has: Pesto, Fusarium Resistant, Asian, Citrus, Fine Leaf, and Purple.
I'm not too sure how to think of these groupings . . . Not all of them are Ocimum basilicum but of those that are, there's still a little randomness.
Johnny's puts the Sweet and Genovese together under Pesto. I am really okay with that. I'd like to think of pesto basil as "sweet." We all have our individual tastes in things (and as herb growers, we really should encourage explorations in that sort of thing

). I'm inclined to prefer Italian Large Leaf here and should note that Nufar is a fusarium resistant type and therefore, more trustworthy in my greenhouse & garden but I grow both.
I don't know if I've ever grown any of these Fine Leaf or Bush basils (altho' I've grown what Richter's claimed was a "compact basil" which didn't turn out that way).
Asian, to me, are the Thai basils. Some of them are purple or have purple stems and flowers. I'd really like to put lime and lemon basils in this group. They seem very similar whether they have purple on them, or not.
Dark Opal and its sisters are purple but my understanding is that Opal is an African basil and not Asian

. Some folks like to use Opal basils in cooking but I don't. I consider it an ornamental. You know, there's nothing wrong with being ornamental

!
I've grown Ararat basil a few times. It is purple . . . Mount Ararat is in Asia . . . still, I'm very inclined to call it an ornamental basil. I think it is very pretty and has a lovely fragrance. I'm just not interested in eating it.
So for me, I like to think of them as:
Italian, for pesto & with tomatoes
Asian, for noodle soups & the citrus-flavored ones for baked fish
Ornamental, for the flower gardens.
Steve

We are each other's harvest; we are each other's business; we are each other's magnitude and bond. ~ Gwendolyn Brooks