assuming a 2 child family and decent money/budget management in each scenario
Poverty - inadequate/damp/unstable housing something has to suffer in order to eat, eg late paying gas bill. This is pretty consistent. Emergencies leave you utterly screwed.
Poor - basic housing (rented) everything is just about covered but it takes masses of knowledge and effort. No savings and very little hope of building up savings. Emergencies mean getting a loan/credit or other outside help and could potentially leave you screwed
Adequate - basic 2 or 3 bed house (rented or owned) everything is covered and a small amount left for saving each month for emergencies
Comfortable - larger/nicer 3 or 4+ bed house, everything is covered, plus nice holidays and savings for fun as well as emergencies
Well off - More than one nice property owned, everything is covered, nice holidays, savings, investments, privately educated kids without worrying about affording it.
Extravagant - Footballer type wealth