What is the difference between 2.4A output with or without Qualcomm Quick Charge 2 or 3?
The various quick charger technologies work changing the voltage provided by the wall (or car) adapter.

The problem is quite simple: if you want to provide 30W to a tablet to power it and charge it, you need a whopping 6A@5V, i.e. a big expensive cable. If the voltage was, say, 15V, you only need 2A, which is feasible.

At the moment, to use quick charge technology you need matching components: if you have an iPhone it won't use qualcomm QC3 tech, but possibly its proprietary adapter use a different QC standard.

Unfortunately, since rising the voltage is out of the USB spec, what happened is that everybody did their own version, and they are not compatible. This will end with USB C.

If your devices implement some sort of QC technology you need to search for a compatible adapter, or you won't be able to fast charge them.