All three are the same system at different scales. A compressor takes in outside air and pushes it into a pipeline. The pipeline holds the air and carries it to where the energy will be used. There the air is released through a turbine that turns a generator, and the cold air leaving the turbine is used for cooling. In the pipeline the air can be stored indefinitely and delivered on demand without energy loss.
What changes is the pipe and what sits at the end of it. A community microgrid uses new pipe laid in a trench through the neighborhood. Pipeline energy storage uses idle steel oil and gas lines over long distances. Data center cooling puts the turbines at the facility, fed on site or by a pipeline.
In each case a natural gas engine drives the compressor first. When solar or wind is added, a renewable-powered motor replaces the engine, and the pipeline and the turbines stay.
How compressed air pipeline energy works