Two stones with the same carat weight get assumed to look the same size once they're set. They don't, because carat measures weight, not visible spread, and those two things move independently of each other.
IGI's own comparison shows this plainly: three round brilliant diamonds, each exactly 1 carat, measured spreads of 6.65mm, 6.45mm and 6.25mm. Same weight, three different diameters, down to how each stone was cut.
Shape adds another variable. Deeper cuts, cushion and princess among them, carry more of their weight in the body of the stone rather than across the top. Viewed from above, that weight reads smaller than the same carat count in a round.
A carat figure on its own says nothing about how a stone will actually look on a hand. Spread and shape do the work the number doesn't.