Impoverished (adjective) according to me is more likely to be used to better describe the circumstances in which a person became poor. As pointed out by Vivi "Impoverished by drought".

I may tell people I'm poor ("I'm broke!"), but I don't say I'm impoverished. Somehow that would seem too pitiful and hopeless an adjective to use. But, unfortunately, "impoverished" does describe some communities in the world.

Impoverished has two meanings: 1, poor enough to need help from others; 2, broken financially. Poor, when talking about living status, it means that people without possessions or wealth. So you could see they all mean poor, but the degree is different. And poor could also mean "pathetic, pitiful", such as the poor girl. Several examples: Money and food were sent to the impoverished drought victims. They clubbed a fund of money for poor children.

Same thing