"Biedermeier Coffeehouse"
The sets are called so because they were made in and around the Biedermeier period, an era in Central Europe between 1815 and 1848.
"Coffeehouse" (wood)
These sets were made in central Europe from ca. mid 19th to mid 20th century. Large sets with reeded balls were typical in use in Vienna Coffeehouses till the 1960s, I believe.
"Coffeehouse" (plastic)
Plastic coffeehouse sets from early 20th century are hard to find.
"Coffeehouse inspired" (glass)