In bar terminology, is there a difference between a call brand and a call drink?

A call brand is a medium to high quality, usually popular, brand of liquor - better than the default well brand, but still below premium (which is also called "top shelf").

A call drink is any mixed drink where the customer specifies the exact brand of liquor to be used instead of just the generic flavor (e.g. "Bacardi cola" instead of "rum and cola". Call drinks are more expensive than their generic counterparts due to the more expensive ingredients.

So basically the call brand is the pure liquor, the call drink the finished product. These two are of course related - a call brand will ever only be served as part of a call drink.

https://redheadoakbarrels.com/bar-drink-ranking-from-bottom-to-top-shelf/