In law there seems to be little difference between caravan and mobile home.
The common characteristic and definition seems to be a structure which is designed or adapted for human habitation and is capable of being moved from one place to another.
Sheds fail, usually missing cookers, beds, taps etc, although they can normally be moved - if they don't fall apart in the process!
I suspect much of this becomes important due to tax and VAT legislation - VAT on caravans is 20%, on mobile homes 5%, possible capital gains tax normally payable on property that is not your main residence, liability for council tax etc.
Fertile ground for tax lawyers!