Ruthenia/Rus (Русь) in ancient times was divided into the Black, the Red and the White Rus. Nobody knows exactly why it was so. There are different theories. Black and White Rus are Republic Belarus (White Rus) now. Red Rus is Ukraine now.
About names:
Russia (
Rossia - Россия) is Ρωσία - a Greek variance of word Русь (Rus'). Now it mean only the RF.
Ruthenia is a Latinization of word Русь (Rus'). Now it mean Kievan Rus (on English) or Transcarpathian Ukraine (on Russian, Рутения).
And the Russian language has such words:
Rusish (Русский - Rusky
) mean Ruthenian, Eastern Slav
and
Russian (Российский - Rosiysky, Россиянин - Rosiyanin, Russian man) mean modern Russian.
Rusin (Русин) is Carpathian Ruthenian man.
Rusich (Русич) is Kievan Ruthenian man.
In English is big confusion: all can be called Russia. In Russian all is clearer.