Basics of smithing,
punchingAfter the metal sheet cools down, it also shrinks a little, so the hole can end up be fraction larger than the punch. Generally speaking the size difference is very, very small, the actual rivets should be skinnier than the punch used for the holes.
If you have seen horned anvil, you've might noticed they often have 2 holes on the face.
One round (pritchel) and one square (hardy), the square is used to place a swage, for bending/working an angle, OR cutting hot bar/rod, sometimes a U fork for bending. The round pritchel hole is there mainly for clearance for punching holes.
There's also some tools with round shank, but they're less stable than square shank in square hardy hole.
Edit: Forgot a warning: Going to the link above at Anvilfire, can lead you to a deep rabbit hole of smithing knowledge and techniques, you might end up building your own forge! Beware.