Student or pupil IDs are not standardized in Germany. Every school and every university has their own thing. Some have cards, some have paper cards. Some of them are laminated, others are not allowed to be laminated1. Some have issue dates, some have validity dates or time spans. Most have no picture. Some schools don't even have IDs at all, but they have full A4 papers or they use simply use the local public transport company's ticket type that's reserved for school children.
Because of that chaotic variety, it's very hard for others to check the legitimacy of those IDs. There are student discounts in most theaters, museums, cinemas and swimming pools, and that list continues.
I would say whether they accept it or not is varying. The fact that you're a student in a different country doesn't usually matter. If it says you are a student and it doesn't have an expiration date in the past, you're usually good. Most cashiers don't much give a damn.
What they do sometimes check is if the name matches your gender, so taking your little sister's student ID to get into the movies cheap might not work if you're big, bearded John and the ID says Jessica.
A lot of places are fine if you have something that resembles a card that has the word student on it if it's from a different country though. Don't sweat it, and enjoy your visit.
1) Deutsche Bahn would refuse the ticket component of the thin paper student ID from Hannover University if you laminated it yourself because their metallic hologram would not be fully usable any more... or so they said. I know people having to pay fines for taking the train without a valid ticket because they tried protecting their ticket from dirt and crumpling