For menu, the word Menü is used. I thought it was more common to use Speisekarte. That's what I was always taught. Am I wrong?
I think that "Speisekarte" is only used for the list of dishes in a restaurant and "Menü" or "Menu" is used to describe a fixed meal, for example "menu of the day" "Tagesmenü". I hope I have helped you :)