And there are also two nouns related to the adjectives you are asking about.

русский (adj) Russian -> русский (noun) (a Russian) - note: this noun has the same form as the adjective.
российский (adj) Russian -> россиянин (noun) (a citizen of Russia) - it is a less common word, though. Some people believe it appeared after the dissolution of the USSR (it was very popular in Yeltsin's public speeches), and they do not like this word due to this reason. But in fact it existed much earlier, even in times of tsarist Russia.

Россияне (plural form) may include: русские (plural form), татары, чуваши, мордва, якуты, буряты, калмыки, ... and nearly 100 other ethnic groups (with their own languages).

I will also provide some examples:

Ivan Petrov lives in Novgorod, Russia. He is both русский and россиянин.
John Smith lives in Denver, Colorado. He is neither русский nor россиянин. He is американец.

Vladimir Popov moved to Denver, Colorado, long time ago, and he obtained the US citizenship. He is not a Russian citizen any longer. He is not россиянин. But he IS русский (his first language is Russian, his parents were Russians, he follows Russian traditions, he considers himself being ethnically Russian).
Ben Forest moved to Novgorod, Russia, long time ago. He obtained the RF citizenship. He is россиянин. But he is not русский unless he insists he is. His first language is English (although he speaks Russian fluently with a slight accent), his parents were Americans, he follows American traditions, he feels related to the American culture etc.