What's a distressed property?

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I've been driving around in my local neighborhood, up and down, side to side, on every street.  There are some properties that I know for sure are distressed.  What I look for is stuff like garbage bag windows, boarded up windows and doors, over-filled mailboxs, unkept garden/flower bed, tall grass and exterior house paint chipping away.

When I've approached some of these houses, many of the home owners were nice people, have no problems with their finances and not looking to sell whatsoever.  There were only a small few actually looking to sell.  So I'm wondering if my perspective of what exactly a distressed property is, is wrong.  

What do you think?  What's a TRUE distressed property?  Could it be that some of the "no problem" home owners actually do have problems and are hiding that information for personal reasons?  Or maybe no problems now, but maybe later?  I know I'm just some random stranger knocking on their door, asking personal questions, so I can understand if they don't want to share such sensitive information.