Not exactly, the "country of turkey" has a lot more lore, and it separates itself from the central-asian turkic culture(s), after entering the middle eastern and anatolian regions. At that point, turkish people were basically totally different from their horse-rider ancestors. However, one thing never changed, they still had huge ambitions to create an empire that will last longer than the average steppe-empires, which had previously been their thing to do when they were bored in the vast steppes. And they were lucky enough that, there was an already built capital city to create a strong economic zone around of, which was held by an at-the-edge-of-death Byzantion.
This image here however, is a reference to the Ergenekon, where according to the legend, the turkic riders that created several steppe-empires, originated from a plato surrounded by mountains, where a boy mated with a she-wolf (as it is drawn in a western furry-style here) and slowly grew larger in numbers. Becoming a tribe of thousands, and leaving the area to search for more suitable land to either live off of, pillage or conquer. You know how it is with steppe empires. Stay around for 25 years or so, pillage the surrounding settled empires/cultures (china, iran, india, whoever you can find, really) and die out afterwards, then start allover again. (The main difference between the turkics, and the mongols though, is that the mongols did not show mercy, while turkics usually did.)
Another detail for you lot, when the Ottoman Empire was really confused about what path to follow to rally around of in the late 1800s and early 1900s, one of the ideas was to unite powers with central-asian turkic nations, by forming Turkestan there. These ambitions were never fullfilled however, because ottomans themselves were busy fighting and loosing wars on all its fronts. And as we know it by now, the empire did not survive the events of the Great War. (Even if it did, the newly formed Soviets already managed to take control of the previously Russian Empire lands once more, and as a result, the steppes are squished between the influence zones of the authoritarian governments of Russia and China today.)
I know too much history to write about. I will just end the nerd-talk here.
This image here however, is a reference to the Ergenekon
I had to google this word and the first 10 results were about "clandestine secular ultra-nationalist organization in Turkey". Was genuinely confused for a while trying to find connection between a furry she-wolf and turkic ultra-nationalists.
So it's safe to assume that the name of this she-wolf is Asena?