I have not yet understood the difference (if any) between the terms российский and русский. I'd like to know whether one is a special case of the other and if the use of the former is old-fashioned. (Dicctionaries only say that российский means Russian.)
To put it simply, русский refers to something ethnically Russian, e.g.
Word российский describes something belonging to Russia:
In other words, русский = Russian while российский = Russia's.
Note that in some cases you can use either word, precisely when you can use either of the two English words above.
Let's begin with российский. It describes anything related to government/politics/geography/bureaucracy or if it is made in Russia. Examples:
- российский паспорт/флаг
- российское гражданство/правительство
- российские границы
- российское оружие
However, with geography, it is better to use the word Russia in Genitiv: горы России, поля России, озера России etc. Also it is more common to say история России (history of Russia) than Российская история (Russian history).
Русский is used in all the other cases. Just to mention something:
- national/ethnic/traditional characteristics (русский народ, русский язык, русская кухня, русские народные сказки);
- cultural aspects (русская литература/словесность, русский балет/театр, русская художественная школа);
- linguistics (русская грамматика, русский язык);
Anyway, how did it happen that there are two adjectives? The fact is that historically our country was called Русь, the stem -рос- and, as a consequence, the word Россия, appeared in the middle of the 15th century under Byzantine impact.
As a conlusion I'll quote a nice analogy from this forum: http://forum.wordreference.com/showthread.php?t=1525097
Российский refers the the country of Russia.
Русский refers to the Russian ethnicity.
These things are completely separate and only by incidence have the same spelling in English. Russian ethnicity is different from Russian citizenship. There are more than a hundred of peoples living in Russia, and the ethnic Russians constitute only about 80% of the population.