A suburb is a residential area that borders a city. The main idea is that it is a residential area. 'Outskirts' means the edge or border just outside any city, town or residential area.. The suburbs are on the outskirts of a city. However, the suburbs have their own outskirts. Also, the outskirts of a small town may have nobody living there, whereas suburbs are definitely inhabited.

The outskirt of a city is the very border or edge of it. Outskirts are not usually as developed as suburban areas. A suburban area is a place not inside the city completely (usually on the border), but is close enough that you can easily access the city from the suburban area. They are usually very developed.