High balls are your "regular" low end/low cost drinks. Generic Rum, white rum, gin, rye, Vodka from the "gun" behind the bar more then likely. Practically Everyone order these. & they are the more common ones served at functions that have a little bar rolled in - like a wedding because they are cheap and popular and convient
they are mixed with the general pops (coke, ginger ale, sprite, soda water, sometimes root beer) or water.
You name the alcohol and then the "Mix"/pop......like "Gin and Tonic", "gin and "sev"/seven up", "rye and coke", "Rum and coke", "White rum and Diet Coke", "vodka and sev"
Now if you get into Cocktails, those get a little more complex......so many ways to mix and match and add, and there is juices and syrups and liquor's. and the price jumps quite a bit. They all have fancy names. "black Russian", "Cotton candy", "sex on the beach", "monkeys lunch", "Cosmopolitan", ........those drinks sometimes have even 2 different ways to be made so that takes experience to figure them out.