How can a woman be a believer and not just a Muslim?

Faith is more encompassing than Islam (submission to God); every believer is a Muslim, but not vice-versa. Faith includes Islam and more; it is belief, word, and deed. Islam is not valid without the root of faith in the heart, just as inner faith is not valid without the outward root of Islam. Absolute and perfect faith is achieved through belief, word, and deed; it increases with obedience and decreases with disobedience. Faith has seventy-odd branches, the highest of which is the declaration "There is no god but Allah," and the lowest is removing a harmful object from the path.