This should help (Longman):
Rich is a very direct way of saying that someone has a lot of money and possessions
• one of the richest women in America
Well-off means fairly rich, so you can buy most things. People are more likely to describe themselves as 'well-off' than 'rich'
• My parents were pretty well-off.
Wealthy is a slightly more formal word meaning rich, especially over a long period of time
• He came from a wealthy family.
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