Both of these words are nouns, and seem similar. However, they are not synonyms.
A housekeeper is someone (usually not a family member) who you pay to come and manage your household. A housekeeper’s responsibilities can be many different things from cleaning and cooking meals, to caring for children and managing basic finances. A housekeeper is a kind of employee.
A housewife is a married woman whose main job is taking care of her family and managing household affairs. She can do the same jobs as a housekeeper, but she is not an employee of the house. She is the boss of the house :).