There's no 1:1 correspondence, but the basics are not so different. "Inside of X" (instead of just "in") and "outside of X" correspond to "innerhalb" and "außerhalb" (Präposition mit Genitiv). Das Verbrechen geschah innerhalb/außerhalb des Gebäudes = The crime happened inside/outside of the building. But you wouldn't say "es ist innerhalb der Kiste" (though it would be understood), you'd just say "es ist in der Kiste". "Inside" and "outside" as adverbs correspond to "drinnen" (short for obsolete "darinnen") und "draußen" ("daraußen"). Same construction as the usual "da + X": "damit", "dafür" etc. Die Kinder spielen drinnen/draußen. = The kids are playing inside/outside. If you use "in" and "out" to describe movement, as an additional complication in German you have to add either "hin-" or "her-": hinein = into s.th., away from the speaker herein = into s.th., towards the speaker hinaus = out of s.th., away from the speaker heraus = out of s.th., towards the speaker. hin und her = to and fro Please come in! = Bitte kommen Sie herein! He left the house and walked down the street = Er ging aus dem Haus heraus und die Straße hinunter. (Observer is obviously in the street). But in modern speaker many people are not aware of the difference between hin- and her-, and so sometimes they are exchanged freely. "Go out" is a bad example, because "to go out and have fun" means "ausgehen". If you want someone to leave your room/your house, you can just say "hinaus!" (a bit old-fashioned). To complicate matters, "heraus" can be shortened to "raus", but "hinaus" is not shortened to "naus" except in some dialects, so the short form is just "geh raus!" or "raus!". You can add hin- and her- to other adverbs, e.g. hierher = hither hierhin dorthin = tither "Dorther" makes no sense, and therefore doesn't exist.

I will try to answer your question. "to come in" and "to go out" are things that people can do, it is a request to do something. You're saying to other people: "Komm herein!" (Maybe into your place.) or "Lass uns ausgehen und tanzen!" (Go out and dance) "I'm in the house" and "It is inside the box" are no actions or request these are stati (? I don't know the plural of "status") or states. Do you get what I mean? You say: "Ich bin im Haus." or "Es ist in der Kiste" I hope this is heplful.