Ordnance Department documentation at the time did not use "Springfield" in the name ("Rifle Musket, Model 1855", for example).
They are sometimes incorrectly referred to as "Springfield rifles".
Rifles have grooves on the inside of their barrels.
The term "Rifled musket" originally referred to smoothbore muskets that later had their barrels rifled for use of the Minié ball.
This term was extended to include weapons that were produced with rifled barrels, as long as the overall design was very similar to the original smoothbore musket.