Manufactured homes are just that - manufactured in a facility and transported as a complete home on axles and wheels that are attached to the I-beam frames underneath.
Modular homes are typically not moved as a complete home, but rather as modules. They are fabricated in a warehouse and moved to a site in modules for final assembly on a foundation.
Because they are assembled on site, modular homes typically must conform to applicable local building codes for the area of assembly. I believe manufactured homes, which can be moved as a total complete unit, only conform to federal guidelines only.