They all refer to the practice of circulating hot water through your plumbing so that you have quick hot water and don waste water running it down the drain while you are waiting. As with most good things there are tradeoffs with hot water recirculation systems.
Hot water recirculation systems are frequently referred to by a variety of names, all meaning attractive much the same thing. Recur pumps, recirculation pumps, re-circulating pumps, and circulation pumps are all the same thing. First, let's examine a basic recirculation system and get recognizable with how it works. The system consists of the water heater, a pump, and a loop of pipe coming from the outlet of the water heater, going from sink to sink in a looped fashion, and returning from the last sink back to the pump which has its outlet connected to either the bay to the water heater or to the drain valve.