We should examine three distinct cases. The first case is that of the numerous Russian-speaking communities outside of the Russian Federation, which do not consider themselves to be ethnic Russians. This is similar to how Irish and Scots speak English but do not consider themselves to be Englishmen. A notable quantity of Russian-speaking Ukrainians and Belorussians have no problem with speaking Russian yet identifying themselves as non-Russian in regards to their ethnicity.
The second group is Russian-speaking communities outside of Russia that do consider themselves to be ethnic Russians, as is the case in Moldova and in the Baltic countries.
The third group consists of native people from the inner Russian republics, including the Tatars, Bashkirs, Erzya, etc. The situation of such people is similar to that of those in Brittany, France. These people have a strong and distinctive sense of national pride, and they don't identify as ethnic Russians while they are within Russia. However, when speaking with somebody who is outside of their country, the majority will casually use term Russian when identifying themselves.
In official language, however, it is more common to use term "россияне" rather than "русские".
So, being back to your question - it heavily depends on context. In particular, Belarusians prefer not to call themselves Russians. But, once again, it depends on how person identifies themselves.