From what I've deduced so far, the fox assigns specific roles to those who enter Folkmore, and each of the three roles possess unique traits shared only among themselves. To me, you fit the role of a Legend with your wings and halo, while a Myth would instead have some form of horn and a tail.

[Oh look, there goes one, which Akechi points to with a gloved finger, over to an obvious Myth strolling by.]

The last one is a touch more nebulous in physical changes, but it's fairly simple to eliminate the other two and land on Familiar as the last remaining.