Modular = looks just like a stick-built (traditional) home, but was premanufactured in a factory, and delivered in just a few massive pieces to the homesite and assembled on a permanent foundation. Generally eligible for normal mortgage financing, though it can vary slightly by bank.
Manufactured = Double-wide or greater "mobile" home, permanently affixed to a foundation on land that is owned. Somewhat restricted financing options and higher rates generally would apply.
Mobile Home = Single-wide mobile home. Not eligible for traditional mortgage financing. May or may not be affixed to a permanent foundation. If no foundation, it's not real estate, it's a metal box being financed (generally at sky-high rates). If on a foundation, still tough to find financing, but would generally be cheaper than on rented lot.
10 years in mortgage banking