Learn English – the difference between “poverty” and “poorness”

I'll tell you one big difference: the frequency :-)

At Google Books:

"poverty is"

About 938,000 results

"poorness is"

About 815 results

"Poorness" is quite rare, by comparison.

Also, that "poverty" is used only in financial contexts is not true. Better dictionaries show:

pov·er·ty noun

1 a : lack or relative lack of money or material possessions : privation, want

transition from a life of almost the greatest pomp and circumstance … to one just, but only just, above the line of genteel poverty — Geoffrey Gorer>

in poverty, morality and even a touch of happiness was possible, never in destitution — R. A. Schermerhorn>

had roamed the picturesque poor quarters … but this ugly, barren poverty on the Spanish land was his first view of some men's helpless fate — Janet Flanner>

b : renunciation as a member of a religious order of the right as an individual to own, to receive by inheritance or gift, or to dispose of property

2 a : meagerness of supply : scarcity, dearth

biographer … is necessarily embarrassed by the poverty of personal information preserved — John Loftis>

the cold thin atmosphere of his work was due … to a poverty of ideas and sensuous imagery — V. L. Parrington>

b : poorness in kind or quality : inferiority

cannot hide poverty of form under an opulent mask of orchestral color — Hunter Mead>

c : lack of desirable elements or attributes : deficiency

the … poverty of North and Northeastern Africa in river-producing power — Samuel Haughton>

suffered … from a certain poverty in our English critical vocabulary — Irving Babbitt>

3 a : debility due to malnutrition : feebleness, emaciation

produce insufficient fodder … and one or two ranches suffered quite heavy losses from poverty — Report: Northern Rhodesia Veterinary Department>

b : lack of fertility

poverty of the soil>

Merriam-Webster Unabridged Dictionary