I’ve seen a good number of listings that were REOs but were not advertised that way. Some of those included a clue about a motivated seller, but others didn’t.
Sometimes the property is described as “lender owned” (not “bank owned”).
Sometimes the only clue that the property is a REO is a statement like in #071093843
“The seller has never occupied the property and is exempt from supplying the buyer with a tds. This home is being sold in its current as is condition. ”
with variations (#086011794)
“Property sold as is … Seller is disclosure exempt.”