There must be a thousand different strains of Brown Turkey figs. So, I can't help you with identification.
However, I bought some of my first trees from Stark, some 37 years ago. After waiting for 10 years or so for my dwarf pear trees to pear, they finally did. But they were not dwarf. They topped out at over twenty feet high
So, I decided not to buy from any one who made me doubt what they would or would not ship; Then about 6 years ago, I read that they had been bought out. So, I decided to give them a second chance, and purchased a Flaming Fury Giant peach.
Then about two years ago it started to bear, and it turned out to be anything but a Flaming Fury giant peach
I really hate paying good money for a plant only to learn years later that it is nothing close to what ordered.
My experience has been when you buy from a lot of online nurseries you may or may not get what you ordered.
I will only buy fig plants and or cuttings from members of this form. Plus, a lot of collectors do not rate Brown Turkey figs that highly.
Hope that helps
Bob, zone 5 Connecticut