What is the purpose of a Citronella dog bark collar?

It depends on the brand and model of Spray Bark Collar you are going to buy. Some No Bark Collars respond solely to the sound of the dogs bark and will activate even when nearby dogs bark. Other models are equipped with a Vibration Sensor which works in conjunction with the sound sensor so that they are only activated when the dog wearing the No Bark Collar is the one barking.

Another View:

The collars will spray in another dog is nearby and barks. I used one on my Doberman and if he was standing next to one of the other dogs who barked it would spray him.