The US. We’d usually use North/South/Central/Latin America for specifics, or if we wanted to imply something happens all over the Americas, then we’d refer to “the entire American continent” or continental America.
The US.
I use both to refer to the USA, since the meaning can be inferred from the context, but use US more often.
We’re all living in Amerika. Coca cola. Wonder-bra.
I read the question and my brain also immediately went to - “Oh, they just listened to Rammstein”.
I would not use „Amerika“ if I would refer to the US. I usually mean the geographical combination of North and South America if I would use the term.
If I want to reference the US, I would use „die USA“, „die Vereinigten Staaten“ or in short just „die Staaten“.