Open bar vs cash bar
At an open bar the host pays; at a cash bar each guest pays for their own drinks. Some events mix the two, for example an open bar for the cocktail hour and a cash bar after dinner.
How is an open bar priced?
Most venues offer a package priced per guest per hour, or a consumption bar where the host pays for each drink served. Packages come in tiers by what is poured, from beer and wine up to premium spirits.
What an open bar means for bartenders
Lines are longer and steadier, so venues usually staff open bars more heavily. Bartenders still check ID and stop serving anyone who is visibly intoxicated; a free bar doesn't change the law.