People always identify them with America because they see them in movies. They used to be really hard to find in Europe when I moved here 10 years ago. We tried getting them for an American themed party but the only places were online specialty shops that sold them for more than 1€/cup.
Now however they can be bought in the grocery store. Still overpriced but reasonable enough.
No, they are premium disposable [0] plastic cups. Most people here had far cheaper versions, when my US roommate brought Solo Cups, I was amazed how thick and stable they were.
[0]: Of course, you don’t dispose them, but that’s their league.