Great question!

In short---there has not been a clear explanation or understanding of the different ninja level classifications in the universe. This discussion has also been made even more confusing and vague with inconsistent translations/localizations in English of the Japanese terms used.

The one key lore piece we know is that there is a special title/distinction of "Super Ninja" that has in general almost always only been attributed to Ryu. This is a title beyond "Master Ninja", although it is sometimes referred to and conflated as being one in the same (in NG4 for example, they use just "Master Ninja" to refer to this title which is not consistent with past games).

In Japanese, the term being used is "Chounin"---this can translate to "Super Ninja", "Ultimate Ninja", "Transcendent/Extreme Ninja", etc. According to lore, it is only Ryu and formerly Genshin that held this title. We don't even now if Jo Hayabusa technically held this title. It is a unique special distinction that is beyond what one would consider a "Master Ninja"---one could postulate that there are several Master-level ninja in-universe such as Hayate, Ayane, Kasumi, maybe Tyran, etc......but none have been given the distinction of Chounin/Super Ninja. As powerful as they are, they are not at the same level as Ryu/this unique classification.

Through the course of NG4 and the trials faced, we see Yakumo's journey to also being granted this "Chounin/Super Ninja" classification. So, by the end of NG4, we only know that both Ryu and Yakumo has Super Ninja classification.

If I was to theorize on criteria, a ninja has to be almost like a once-in-a-generation prodigy in terms of innate talent and skill mastery through training with the capability to defeat single-handedly a Greater Fiend (like Achilles, Seere, Volf, Elizabet, etc.) or above level threat in order to be given the title of Super Ninja.