Enroute enviroment, All of our sectors have an R-side and a D-side. The guy you're talking to is the R-side, the D-side is sitting next to him helping with the coordination and other stuff to keep the R side on the radios and eyes on the scope as much as possible. If there is no D-side, the R side is working both the R and D functions by himself, and thats where 'Sorry, i was on the landline' comes from. At least in my area at my facility, the R side is working alone 85%+ of the time.
When you train, you go through all the D-sides first, then back upstairs for R side school. Our staffing isn't good enough to have D-sides on a normal session, so you generally only have one when theres a trainee working on that sector, or if you're really busy and ask the Sup for a D-side. Obviously taking a CPC as a D side is taking away a break from an R-side, so when it slows down again you'll generally release the D side and go back to 'One Holing it', aka working the sector alone.
Theres some times where its so busy and theres so much going on at the sector that you really need a D side just to take some of the phone calls and evaluate handoffs for traffic conflicts, so the R side can work the traffic already in the sector.
At least in enroute, we have another position called the 'Tracker' or 'Overhead'. That person is plugged in and literally just a third set of eyes on the scope. Ive never seen it actually used in anything other than a training scenario.
https://www.kongsberggeospatial.com/images/capabilities/atc.jpg
If you look at that image, its 4 R sides working a sector alone. The D side would sit in front of that second keyboard, and manage the little screen kind of tucked away off the right hand side there. That screen has all the Flight Plans and info for aircraft projected to enter the sector in the next 20-30 minutes or so.