The U.S. 1st Infantry Division's nickname is the title of Call of Duty 2: Big Red One. Treyarch's 2005 console shooter follows that division and was not a PC expansion of the computer game that shares the numeral.
North Africa, Sicily, and the push into Europe give one squad a continuous war instead of a montage of unrelated heroes. The "Big Red One" shoulder patch is the through-line, so the player stays with the same unit's campaign.
Other Call of Duty stories jumped nation every few missions. This console campaign sticks with the American division whose nickname is painted on the box.