My understanding of the roles that are different:
The Exec or First Officer - Actually, Spock fulfilling this role and the role of Chief Science Officer in the original series was due to his Vulcan intelligence and constitution. Ordinarily, First Officer was a separate position. The Captain may lay out a game plan, so to speak, and give an order to the Exec to carry it out, and then the Exec gives all the detailed orders to the crew to make it happen. The Exec does crew evaluations with the ship's counselor, and the job really seems to be a way to allow a promising officer to understudy with a seasoned captain pending becoming a captain themselves.
Flight Controller (Conn) - I guess due to better computers, one person is now able to perform the functions of the old Helm and Nav stations.
Operations (Ops) - Resource management, including human resources. This included the Science department, and if there is still a Chief Science Officer, he/she/it no longer has a station on the bridge, but apparently relays information to the Ops officer, like many other departments do. (When Data's hands were moving across the controls on his station, he may have been rerouting power from phasers to shields while directing the Science department to focus sensors on specific points of interest in the area - such as an enemy vessel - while also filling out a requisition order to Starfleet for more Cardassian hair gel in response to a message from Mr. Mott, while ALSO sending a request to Chief O'Brien to have someone from his team look at a malfunctioning 'fresher in Crewman Hall's quarters.)
Counselor - Presumably at some point, Starfleet decided that while McCoy's method of getting them tipsy/drunk and getting them to talk it out may have worked fairly well in the past, perhaps having someone actually trained in psychology and other mental medical disciplines on board might not be a bad idea. I don't recall it ever being stated directly, but the Counselor *does* report to the CMO, probably as a sub-department chief like the Recreation Officer Harb Tanzer was in some of the TOS novels.
Security Chief/Tactical Officer - I'm not sure that these are generally embodied in the same person on most ships: this may be a case of Worf being exceptional like Spock and Scotty were in TOS (I'm not sure that the Chief Engineer was also the Security Chief on every ship in TOS, either). But the Security Chief's job is to command internal security and away team security, and the Tactical Officer's job is targeting and firing weapons, and they have some amount of command over the weapons crew, as well. And for some damn reason, Worf answers the phone, too, even though that seems like it's a job that should either belong to a Communication's Officer, or to Ops in conjunction with a Communication's Department that like Science has no regular seat on the bridge.