HUD (federal agency called Housing and Urban Development) homes are homes where the mortgage is guaranteed by HUD. So, when the bank forecloses, HUD pays the mortgage off, seizes the property, and then sells the home to recoup their losses. A foreclosure sale is when the lender forecloses on an owner, seizes the property, and then sells it to recoup their losses.

a foreclosure is any prop for sale when its lender is not being pad.

a HUD home is a specific FED insured home for sale.
[all HUD homes are foreclosures, not all foreclosures are
HUD homes]