User blog comment:Trainguy0217/Battlefield 3, Bad Company 1 and 2, and Battllefield 4 connected?/@comment-4386751-20190414174551

Consensus thus far is that they are not. Battlefield 3 and 4 are the only games to have continuity, while the Bad Company games may not even relate to each other given that the events of BC1 were never referred to in the sequel.

Also, the Russo-American Wars are never referred to in game as World War III.