Coins that did not fall directly under the stamping 'dies' are called "off-center"coins.
Here is an example of such an error where the coin involved is a 19th century Flying Eagle cent, the first modern size penny issued.
Previously, pennies were copper and the size of a quarter.
Off center errors occur in all denominations and also in the early years of U. S. coinage.
A few examples from the archive follows:
2 cent piece
3 cent in Nickel
20 cent piece
3 cent in Silver
.... Also See Shield Nickel with Rays
Half Dime rev. & obv.
Seated Liberty Dime
Barber Quarter - and - Seated Quarter
Standing Liberty Quarter
See our Bust Half Dollar
Eighteenth Century Half Dollar - and - Barber Half Dollar
Walking Liberty Half Dollar
See our Franklin Half Collection
See our Walking Liberty Half Collection
See the other known Off Center Morgan Dollars
Also see major off center Roman coins
Also see major off center Mexican Eight Reales