Focusing on the "bad" ...
In AmE:
A working class neighborhood is typically not considered a "bad part of town". These neighborhoods usually have relatively lower rates of violent crime and drug abuse, and the housing stock is usually well-maintained, with a relatively higher number of homeowners; trash removal by the city is regular, and there are usually nearby conveniences such as food markets.
A "bad neighborhood" typically has a high rate of violent crime and drug abuse, and the housing stock is poorly maintained, often by "absentee landlords" who allow their rental properties to become derelict; trash removal and other municipal services are less reliable and refuse can build up on the streets; there are few conveniences. These neighborhoods are often located in what have been called "food deserts", where access to fresh foods is limited.
"The boondocks" and colloquially "the boonies" are rural. Population density is lower. Violent crime rates are usually much lower than they are in urban "bad neighborhoods", but a good many rural communities have been hard hit by recreational drug abuse, methamphetamine and heroine. Sometimes the housing stock is ramshackle, but not necessarily so. Food markets are usually quite a distance away. These areas are rarely given over to subsistence farming. Trash removal is not handled by the municipality but by private contractors, and so in rural communities one often sees discarded items on the properties which would have been removed on "large trash pickup day" in a suburb.
"The projects" are government-run rent-subsidized dwellings, sometimes low-rise, sometimes high-rise, usually found in urban centers. Many of them have high rates of violent crime and and drug abuse and they are often found in or near "bad neighborhoods".
