Can someone explain the differences between using an air compressor after cooler with filters versus using an after cooler and dryer with filters?
If this hot, wet, compressed air is passed through an after cooler, the air temperature drops. As a result, the compressed air can "carry" less moisture, and the air naturally starts to become dryer.
Downstream from the after cooler a general purpose compressed air filter will strip much of the free water (actual liquid) from the air stream, furthering the work the after cooler has done.
At this point, and depending on how dry the compressed air has to be for your use (remember, the dryer it is the higher the cost to make it so) sometimes the compressed air is run through a dryer.
Dryers work better with cooler compressed air, so it makes sense then, if your compressor is working hard and pumping really hot air into the mains, that this air gets passed through an after cooler before it gets to the dryer.
Consider your compressed air "wetness" as a line from wettest to driest. At the "wettest" end you have the compressor, and the driest end the application that is using the air.
In order to get the compressed air dry enough for your application, you will place drying equipment between your application and the wet compressed air source, the compressor.
Working from the compressor to your application, you will commonly see after cooler(s), general purpose filters, refrigerant or desiccant air driers, more general purpose filters, point of use air dryers, another air filter and so on.
You will need to keep treating your compressed air with drying equipment until it reaches your point of use as dry as it needs to be for you.
That's why some plants have tons of "air-treatment" equipment, and others have less.
Hope this helps.