You’re right, they appear to be the same thing, but I believe there is one technical difference. Since Regulation Z doesn’t provide a definition of mobile home for us to use, I’m looking to the industry and HUD standard. There were mobile/manufactured home building standards implemented by HUD in 1976 under 24 CFR 3280. Mobile home is the term applied when built before these standards were implemented. Homes produced after implementation are called manufactured homes.
Here’s a couple of links that may help:
https://www.nadaguides.com/Manufactured-Homes/Tips-and-Articles/Definitions
https://portal.hud.gov/hudportal/HUD?src=/program_offices/housing/ramh/mhs/faq
And remember not to confuse these with a modular home, which is different as well.