Manufactured housing is a type of prefabricated housing

Prefabricated home

Prefabricated homes, often referred to as prefab homes, are dwellings manufactured off-site in advance, usually in standard sections that can be easily shipped and assembled....

 that is largely assembled in factories

Factory

A factory or manufacturing plant is an industrial building where laborers manufacture goods or supervise machines processing one product into another. Most modern factories have large warehouses or warehouse-like facilities that contain heavy equipment used for assembly line production...

 and then transported to sites of use. The definition of the term in the United States is regulated by federal law (Code of Federal Regulations, 24 CFR 3280): "Manufactured homes are built as dwelling units of at least 320 square feet (29.7 m²) in size with a permanent chassis to assure the initial and continued transportability of the home." The requirement to have a wheeled chassis permanently attached differentiates "manufactured housing" from other types of prefabricated homes, such as modular homes.
According to the Manufactured Housing Institute’s National Communities Council (MHINCC), manufactured homes

are homes built entirely in the factory under a federal building code administered by the U.S.