Doma is to Othard as Gridania is to Eorzea. Othard is the continent that holds Doma, so they aren't mutually exclusive. Doma is just a region of the whole.

However judging from Yugiri's hesitation to show her face, she must have encountered quite a bit of predjudice in the past so it's understandable that she might not be a familiar race to Domans as a whole.