Answer:
'Miss' is the older of the two terms, and it is traditionally used as the form of address for an unmarried girl or woman (whereas 'Mrs.' is used strictly for married women)
During the women's movement, it was argued that having separate titles for married and unmarried is sexist, since all men--married and unmarried-are called 'Mr.' 'Ms.' gained popularity as a 'one-size-fits-all' title for women, regardless of marital status.
Nowadays, 'Ms.' is a safe option for all women (and 'Miss' for girls under 18), but some may tell you that they prefer to go by 'Miss'.