Outdoors (you normally add an "s") vs. Indoors
Outdoors means in nature, not inside any buildings; for example, sometimes, we describe nature as "the great outdoors"
Indoors means inside of some type of buiding; for example, "we should be indoors during this bad weather"
Outside vs. Inside
Outside means not "in"; for example, "the shoe is outside of the shoe box" (the shoe is beside its shoe box); it can also mean outdoors; for example, "let's go play outside" (outside can mean in the front yard)
Inside means not "out"; so, for example, "the spider is inside of my shoe"; it can also mean indoors; for example, "let's go back inside. It's too hot out here"