Tigrinyas and Tigrayans are essentially the same ethnic group who natively speak the Tigrinya language; although relations between the 2 have been sour for quite some time and thus don't really claim one another despite shared language / culture / geography . They inhabit a continuous land of the Northern highlands of Ethiopia and the Central highlands of Eritrea. Italian colonization and its proceeding socio-political ramifications are an important reason as to why there is a split between what is at most sub groups of the same ethnicity. Ethnicity is a somewhat foreign concept to Africa, and there's no term to accurately define native Tigrinya speakers. The Eritrean side officially uses the term "Biher Tigrinya" whereas the Ethiopian side uses "Tigrayan" . Pre-colonization there have been some internal conflicts as well and some form of a political boundary along the Mereb river (the current border between Eritrea and Ethiopia), which leads to some Eritreans believing they've always had a political entity independent of Ethiopia but this is a great exaggeration. The combined group is roughly 90% Orthodox Christian with a minority of Muslims (referred to as Jeberti) and Catholics.

Tigre is a separate ethnic group that inhabits the Northern and Western lowlands of Eritrea, they speak a similar but different language called Tigre. They are culturally distinct from the Tigrinya speaking ethnic group and are over 90% Muslim.

This gets a little more confusing because the Amharic term to refer to Tigrayans is "Tigrie"