I think in the industry manufactured homes refer primarily to single and double wide trailers, while modular homes are sections built in a factory, trucked to the site, and bolted together.
I think they all come under the heading of prefabricated homes, and have been around in various forms for a long time.
I think the first big push into prefabricated homes was by Sears, which offered complete homes in a variety of styles, starting in the early 1900s, with Montgomery Ward soon following.
They included everything you would need to install the home, with everything precut and staged and packed into pre-numbered bundles and crates so that you'd just follow the numbered instructions.
I'm pretty sure that you could even buy home furnishing kits to compliment your new home, which included paint, furniture, and other accessories like wall decorations and window treatments.