How many rings would the average person have other than their wedding ring or band? They might have a college ring but isn't worth stealing (initials, graduation year, sometimes a name, all easily identifiable by a pawn shop) unless you can melt it down or have a trusted source that can do that job. We don't have much in the way of jewelry but our parents do and they only have their wedding rings/bands and college rings.
If someone did have other rings, I'd think they'd be visually different, wedding rings typically have one large diamond set with other jewels and a band is dead obvious as it's so plain. A ring with multiple small diamonds or other gemstones (emerald, ruby, etc) would almost always be a safe bet, especially if a ring similar to the traditional wedding ring was available for comparison.