Are "trade-off" and "compromise" the same thing?

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I would say a compromise involves two or more parties having to adjust what they're asking for / amend their position in order to achieve an amicable result. A trade-off, on the other hand, doesn't have to directly involve more than one party.

For example, I might be torn between choosing to study at one university or another, and both options involve a trade-off or trade-offs, i.e. both options entail pros as well as cons. In this example, the universities aren't directly involved in my dilemma; I'm not entering into a compromise with them. "There are always trade-offs" entspricht in etwa dem deutschen "irgendwo muss man Abstriche machen."