Lead shot is made by pouring molten lead through copper screens or sieves. The size of the the mesh roughly determines the shot size. As the molten lead falls in the high shot tower, the molten droplets become spherical and begin to harden. They fall into water to completely solidify and cool. Then they are dried, and may be coated with graphite before further processing for size. This final size sorting is done by passing them through screens or sieves with the nominal sized openings, or by sorters that allow the shot to roll across rods with openings between them that gradually widen until the opening is large enough that the shot falls through.
Naturally, this means that there is some tolerance within any given size. So American no. 7 1/2 shot may measure slightly over or under the nominal size of .090" diameter, which helps to explain why actual shot count for a 1 oz. volume will not always be identical. The alloy of the shot is another factor because the density of the shot may be different. There are numerous sources in print or the internet to find the nominal weight and diameter of all common shot sizes, and the differences found in different countries.
Shot size matters due to various factors such as pattern density, range, and how tough the target is to break or kill. Larger shot has greater mass, and retains energy better, so it will kill better at longer ranges. This all assumes that there are not sufficient holes in the pattern to completely miss the target, or merely strike a less lethal spot. By now, most of us should understand that we have a much better chance on a 40 yards straight away shot of dropping a large ringneck pheasant with heavier winter plumage, with # 5 lead shot than # 8 lead shot at equal velocity. Some critters are just naturally tougher to kill than others, so more retained energy and better penetration may be needed to avoid crippling losses. But several other things matter, such as choke and pattern density... and actually being a good enough shot to have the bird solidly within the pattern. And there is a greater chance that the same load of # 5's at the same range might allow a dove or clay target on edge to slip through unharmed. The expert in Parabola's video mentioned the fact that making an intelligent choice of shot size may instill confidence, and that too will improve scores on game or clay targets.
