Yes and no, it depends on the equipment and the controller. Most (if not all) aquarium controllers have "switched outlets" So what ever is plugged into the outlet can be turned on or off by the controller turning the outlet on or off. The controller will have a clock, so the outlet can be switched on or off on a time schedule. Through additional modules, probes and switches, the outlet can be switched on or off through other parameter IE: temp probe. when the temp drops below a certain temp, turn the outlet on and at a certain temp turn it off, for heater. Or when float switch 1 is off turn the outlet powering the pump on. Some controllers have modules for more controllable functionality. The Neptue has a module for the vortech pump so throughout the day I can program different modes and flow percentages automatically. In other words have lagoon at 50% power overnight, and then 60% NTM in the AM and 80% NTM in the afternoon and so on.
It's mostly a toy, almost nobody needs a controller, but I'll never be without one again, I love it. I changed from the ReefKeeper lite to the Neptune Apex for the Vortech control. ReefKeeper should eventually offer it also but they are a little behind.
I do believe it is a good idea for a controller for heater, it's good insurance to keep a heater from sticking on and frying a tank. A basic controller for this purpose and is expandable to do a lot more is only $119.