A dictionary will tell you that they mean broadly the same thing:
housewife noun (plural housewives)
1a married woman whose main occupation is caring for her family, managing household affairs, and doing housework:
the traditional division of labour between the husband as breadwinner and wife as housewife
I am not just a housewife, I am an accountant, nurse, negotiator, cook, driver
chiefly North American
a person, especially a woman, who manages a home.
There might be a difference in emphasis. The word housewife focuses on the state of the woman [it must be a woman!] as a wife. There may be a slighty pejorative notion (cf fishwife). Homemaker is a more modern word — OED attests it from 1861 rather than the thirteenth century for housewife — and it focuses on creating a home rather than simply being in a house. And it's sex-agnostic.
However, which is used is entirely a matter of style and choice, perhaps with a regional bias.