The Japanese word 武者 meaning "Warrior" is composed of the kanji武 (read mu) meaning "Warrior; Military" and 者 (read sha) meaning "Person". The first kanji 武 is the same kanji used in Way of the Warrior (bushidou) and so musha implies a warrior in the Bushido tradition.
Incidently, 武者 is the same kanji used in the title of Akira Kurosawa's film Kagemusha meaning "Shadow Warrior".