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
Buffalo Nickel 3 cent in Silver Shield Nickel .... Also See Shield Nickel with Rays

Barber Dime 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

Morgan Dollar
See the other known Off Center Morgan Dollars

Also see major off center Roman coins

Also see major off center Mexican Eight Reales