The word ‘monk’ comes from the Greek μοναχός which means ‘alone’. A monk is someone who lives alone. Are all people who live alone monks? No. Do all monks live alone? No. Then what does the word ‘monk’ mean?
In the Orthodox service of consecration of a monk, the person about to become a monk is asked: ‘Why have you come here falling down before the Holy Altar?’ You see, a monk is someone who consecrates himself to God. The answer that the would-be monk gives is this: ‘I desire the life of asceticism.’ The person consecrating himself to God desires the life of asceticism. The life of asceticism is the road to God.
In the Orthodox Church, the service of tonsure, of consecration of a person to God as a monk, is exactly the same for men and for women. There is no difference.