To know the difference, we must examine the cut of a men's suit. In the British American tradition, there are only two silhouettes that have historically been cut into suit patterns.
The American cut is a 3 button, natural shoulder jacket, with a notched lapel, and a welt upper pocket and flap pockets below. The jacket is vented in the center back. The top button is not buttoned, but is actually on a part of the lapel, which is rolled, so that the jacket fastens at the middle button only, as the bottom button is left open.
The top buttonhole is finished on both sides and is intended to be seen. The shoulders of this silhouette are soft and gently sloping. The stance of the fastened button is higher than the waist, and the jacket itself is not darted inward to the waist, so that the entire look is one of comfort, but rather square in shape.
Though this pattern does not follow the body's shape, it is easy fitting, with wider armholes. In its most traditional form, this silhouette has a "sack" shape, almost boxlike. It is usually paired with straight front trousers with cuffs, and the trousers do not break (fall forward with a crease) on the shoe.
The British cut is a 2 button, natural shoulder jacket, with a notched lapel, and a welt upper pocket, with flap pockets below. The top button is buttoned, and the lower button is left unbuttoned. The stance of the fastened button is to the waist, for a longer, more graceful look than the American sack jacket.
Several other aspects of the silhouette accentuate this longer look: first, the jacket is slightly tapered at the waist by darting. Secondly, the shoulders, while soft, are a bit more shaped than the American model. The armholes are higher to the arm, and there are two side vents in the back. All of these elements conspire to give the appearance that the jacket conforms to the lines of the body, though not rigidly.
In fact, typical of English jackets is the "blade" which is the fold beside the shoulder attachment on the back of the jacket, which provides the extra fabric for ease of movement. The British jacket is typically paired with pleated trousers, slightly tapered, whose cuffs break to cover about 2/3 of the shoe.
There is also another British style widely admired in America - the double-breasted suit, gently tapered, with a firm but natural shoulder, and side rear vents. This style buttons one, second from the bottom button, out of six front buttons.
Keep in mind that a double-breasted jacket is always buttoned! Some double-breasted jackets are cut to fasten at the lowest button only. This is a result of a style made popular by the Duke of Kent, the brother of David, the Duke of Windsor.
It allows for a longer look, as the lapel appears longer. The lapels are peaked, the upper pocket is welted, and the lower pockets are either flap or inset besom. The trousers are pleated.