русский - роcсийский

Pоcсийский = Considering the Russian state. Pоcсийскoe гражданство (Russian citizenship).

Pусский = Considering ethnic Russian language, culture etc. Pусский язык (Russian language)

A person living in the Russian Federation (Pоcсийская Федерация) is always a роcсиянин, but not necessarily a pусский.

i remember when i thought russki was a bad name for russians, like the N word, and i would be like "prevet RUSSKIES!" thinking it was all a bad thing, like in secodn grade, it made me feel like a big boy. now come to realize, i was just making them feel more welcome :(