Air Force 1 has some of the same communications equipment as an E-4B, but its core mission is executive transport (with press onboard and everything). The E-4B is a dedicated command center. Lots of communication and data connectivity equipment. No seats for the press.
In short, AF1 carries the President and his entourage. The E-4B carries the Generals and their staff.
Both aircraft are based on the 747 airframe.