Mobile home is the everyday name most commonly used for what the housing industry and regulators formally call a manufactured (mobile) home: a dwelling built in a factory on a permanent chassis and then moved to its site. The two terms describe the same category of housing.
The name "mobile home" is older and dates to a time before factory-built housing standards were formalised; "manufactured home" is the term used in building codes, federal regulation and most modern lending and insurance documents. Both still appear side by side in everyday use, insurance policies and flood-insurance eligibility rules.
For how these homes are financed, insured and made eligible for flood coverage, see the main Manufactured (Mobile) Home entry.