Working Dog Training collars v's Companion dog training collars
Remote trainers, is a common phrase that is used to describe a training collar that is activated by remote control. The system typically sends a radio signal to the collar. There are several tools available on the remote control, for example most systems have an audible tone, which means nothing to the dog until you teach the dog what the audible tone means. Maybe you could beep the collar every time you give the recall command, so if your dog is far from you, just press the beep button. Obviously a dog getting into a garbage bin, or jumping up on visitors (especially if they are wearing white pants) can be easily deterred with a correction right at the time of the misdeed. These types of systems are companion dog training collars don't need long range, unless you are taking your dog to a beach or park, probably up to 400 meters range would do the trick.
Hunting and mustering dog training collars long range or working dog training collars for sheep and cattle dogs need extra range, so depending on your situation will mean different range requirements. A sheepdog on flat terrain without many trees, might need an 800 meters range but a hunting or cattle dog in hilly terrain with lots of trees, might need the longer range of 1200 to 1600 meters. Not that you are training at these distances, its just a way of classifying the strength of the transmitter and buying the system that suits you best.