Aaron, my understanding is (hope it doesn't come off as snobby, it's just MY understanding)....
Negronne: umbrella term (and perhaps the correct term as used by French collectors ...see Baud) for what that Americans call Violette de Bordeaux (VdB).
Petite Negri is the term for the dwarf variety of Negronne (or a close sibling) as named by a gentleman associated with Edible Landscapes. It has been suggested that Petite Negri was originally given to Black Ischia a century ago, but EL resurrected the name for its dwarf Negronne offering (because the name is good for a dark dwarf variety). In the US, Petite Negri should only be used for the dwarf Negronne/VdB type tree (as issued by EL, etc.) To add some confusion, The Vista Mission is not a Black Mission. It has been since genetically matched to the Negronne/VdB family. Jon V. has mentioned this in several postings. I don't know of any case where the term Negronne should be appropriately be associated with the "true" Black Mission/Franciscan fig. As a note, Negronne should not be a catch-all for all Bordeaux figs (Ronde dB and Rouge dB are completely different). Also, according to UCD, Beer's Black is a Negronne/VdB type.
Black Jack should probably be used only for the dwarf California Brown Turkey...but it's a catchy name and I'm sure a number of local growers might have used the term over the years for different varieties.
I don't know what to make of the photo and description of the "Petite Negra" on Logee's website. Other than it means "Little Black." If the picture is true, it's not the same as Petite Negri. It is probably the dwarf Turkey/Black Jack. I wouldn't buy it simply because it makes me think they have no idea what they're selling (unless I was just curious and didn't mind getting a *surprise* fig).
If you haven't seen it, here's UCDs genotype results. Keep in mind, if a scion was misnamed when submitted, errors would of course occur in the results. Also keep in mind that being a 99% match doesn't mean the trees are identical...someone pointed out that people and monkeys are 99% the same ;)
http://figs4fun.com/Links/FigLink1110.pdf UCDs method was to make several markers in the DNA strand and try to match sections of the strand...this is different that genome matching the entire DNA strand. But it's an interesting and useful way to get some grasp on synonymity and also rule out some cultivars that seem to look a lot alike but maybe be genetically VERY different.
Hope this helps...it's about all I can add this thread. The rest we'll just enjoy as part of the romance and adventure of gardening/figging :)