"Outside" is any place that is not "inside." It can mean "out of doors / not in a building / in nature." It doesn't have to be a physical space though. Something can also be "outside of the discussion" ..not meaningful to or a part of the discussion. "Outskirts" is a noun. It is usually used in the phrase "the outskirts of the city" the area that is "outside" of the city or away from the center of the city. I've never heard it used as a singular before.

Well, they share the same meaning. However, outskirts is basically used to refer to the outer parts of a town or city where "outside" has a broader meaning.