A beverage-service system where guests/attendees pay for their drinks is known as a cash bar.
Don’t even think about suggesting a cash bar as an option for a wedding (unless you’re in the UK where, apparently, wedding guests are accustomed to paying for their drinks at private social events)!
A cash bar will catch most US wedding guests off-guard. Instead, suggest that your clients serve a signature cocktail or beer and wine, only.
The opposite of a cash bar is an open bar.