In a simple assay (ie a one step assay, like a Burkholder) if there is a colony in the middle of the zone of inhibition, it could be phage or bacteriocin (or something else, sometimes). If you take a bit of the zone of inhibition and use it to start a plaque assay proper, then you can tell the difference; a phage plaque propagates without the bacteria (filterable, self-replicating) while bacteriocins will dilute away if there is no colony formation. Practically speaking, if you put phage in low dilution into an inoculum you will get multiple plaques of similar scale; if you do this with bacteriocin, you get even thinning of the lawn at the different dilutions.
Mind you, defective phage (phage tails, pyocins) vs microcins vs classic globular colicins, etc cannot be differentiated this way. That's a size/structure determination, ultimately.
Also, if you want to do another differentiation, you can take a bit of the zone of inhibition and look for phage sized particles with DNA using DAPI or AO; but be careful, there may be other DNA associated extracellular particles; eventually, electron microscopy is the best strategy.