I can answer for British English. Suburb: a residential (usually) area surrounding a city, not in the centre but still a part of the city. Croydon, for example, is a part of London but isn't anywhere near the London Eye or Buckingham Palace. Countryside: a rural area, not near any large cities, and usually isolated altogether from large-scale industrial and urban development. Think farms, fields, a vastness of trees and land.

google "what is the difference between countryside and suburb?" https://wikidiff.com/countryside/suburb https://www.italki.com/question/140220

In the United States, "countryside," or "the country," represents an area with low population density--with few buildings, few residents, and small isolated towns--usually covered with fields and farms. Referring just to everyday language, not strict definitions: A "suburb" is a populated community that is close to, and culturally and economically connected with a city. A suburb has its own name, post office, schools, and local government. Many suburbs are "bedroom communities." The people in them work in the city and "commute" daily by car or by train. The typical situation in the United States is a city, surrounded by suburbs, surrounded by "the country." The city has tall buildings, dense housing, and is a business and cultural center. The people in it range from very wealthy to poor. It is an "urban" area. Surrounding the city are "suburbs," with separate single-family houses and lawns. Farther out you get "out in the country," which is a "rural" area. In the United States, what we call "the suburbs" are often really "exurbs" according to the strict literal definition of the word. However, "exurb" is an obscure word, not used in daily speech; don't use it. I think the contrasting words "town and country" come from British use, when a wealthy person owned a "town house" in London and a "country house" out in the country, and regularly moved between the two. "Vacation"' was the time when you vacated the town house and moved to the country house.