The term "privatization" refers to the process that implies moving services or similar from public or government to the private section. This implies services formerly provided by the government are transferred to private businesses that are in charge of providing the same services. This occurs in sectors such as education or prison management in which the state decides to pay to private companies or entities to provide services that are in charge of the government. This term is the opposite of "nationalization" in which private services or sector become public. Considering this, the one that occurs when private businesses are allowed to supply services that government provided is privatization.
This means that public services such as bathrooms or water fountains could still be whites only or blacks only but they had to be equal in quality. (i.e the bathroom for whites only could not be very clean and fancy while the blacks only bathroom was dirty).