"British ball" or "British Open ball" was the term for it most commonly used by American golfers and fans because those golfers typically only encountered the ball during the Open Championship. To golfers playing under R&A rules, it was simply the "small ball."
The British ball weighed the same as golf balls approved for play by the USGA - 1.62 ounces. On weight, the R&A and USGA agreed. But the "British ball" was very slightly smaller in size, with a diameter of 1.62 inches, compared to the USGA minimum of 1.68 inches. The R&A approved the smaller ball when it first appeared, but in the early 1930s the USGA ruled against the smaller ball, sticking with a minimum diameter of 1.68 inches.
The smaller ball was an option for golfers playing under R&A rules; it was not an option for golfers playing under USGA rules.
But American golfers almost unanimously preferred the smaller ball when playing in the British Open. Arnold Palmer, Jack Nicklaus, et.al., all switched to the British ball when they played the Open Championship (or any other competition governed by R&A rules). The smaller ball went farther and was more workable in the wind.
But over the years, a desire grew to standardize the rules on golf ball size. In 1974, the R&A outlawed the small ball in British Opens, but it wasn't until 1990 that the R&A adopted the USGA's 1.68-inch minimum diameter rule, relegating the small ball to history.
