At least as used in California:
Suburbs — an area on the outskirts of a city, or small town/city that is close to a larger city, that mostly consists of housing and businesses that serve the local residents. The suburban area won’t have major centers of employment or high-rise buildings, usually. People often live in the suburban area — because houses are bigger, schools are better, the area is prettier, etc. — then commute into “the city” to work. If you have high rise buildings, noisy streets, and nowhere to park — you are probably in “the city.” If you have the opposite, you are probably in “the ‘burbs.”
Countryside — this is an area farther away from any urban center. There are few houses and a lot of open, undeveloped land. There may be farms, or maybe just empty land. But houses will be far apart.
Outskirts — an area on the edge of a city or town. For example, when driving into a city from the countryside, the first part of the city that you reach is not the downtown, city-center. It’s the outskirts. It probably is less crowded than the center.