Hi alanabit - There are a lot of names for different kinds of Glühwein or punches. I can give you a short and surely incomplete list of names used here, but in Austria there can be used local names not known over here.
punch = Punsch (East Indian: five)with water, tea, lemon, arrack, sugar (the classical preparation.
If the sugar is dripping in burning, we call it Feuerzangen-Bowle = lit. tong bowl = burnt punch.
Nowadays instead of tea a strong red wine is used, and rum instead of arrack

Any hot spiced wine is called Glühwein = lit. glowing wine.
Now obsolete distinctions were made in former times according to the colours of clerical garments:
- Bischof = bishop, from white wine, and
- Kardinal = cardinal, from red wine.

Prost
Wilfried