PD 3.0
The original PD 2.0 standard initially supported 5V, 12V and 20V but 12V was a bit too high for devices to fast charge batteries and a bit too low for devices which can be used in cars as when running a car battery is typically about 14.4V. So 9V and 15V was added and 12V was deprecated. Some supplies may still support 12V though.
Programmable Power Supply (PPS)
This is an optional extension to the PD 3.0 standard and allows to device being charged to request a different voltage and also a higher current. The voltage requested can be between 3.3V and 21V in 20mV increments. This is commonly used in battery fast chargers and for example the Samsung Note 10+ requests 10V at 4.5A when doing a super fast charge. Without PPS support the next PD profile would be chosen which would be 9V at 3A so 27W instead of 45W.
E-marker
Regular USB-C cables are only rated at a 3A charge current and 480Mbps bandwidth which is less bandwidth than USB3 cables. Cables can be rated for higher bandwidths and charge currents but these need a chip in the cable to tell the devices the cable supports faster data transfer and can safely handle higher charge currents.
A standard cable is rated at 3A and is commonly referred to as a 60W cable as 20V at 3A is the maximum it can support. Higher rated cables support up to 5A and are commonly marked as 100W cables and must have the E-marker chip fitted.
This is however quite confusing as a device which supports PPS can provide more than 3A at power levels less than 45W. A Samsung phone which wants to super fast charge at 10V 4.5A would require a 100W cable in order to get more than the 3A of current even though it is only drawing 45W. Another common confusion is a laptop which wants a 65W charger. Often people use a third party USB-C supply which is rated at 65W and leave a bad review when their laptop reports it is not charging at the full 65W. Most likely the charger is fine but they are using a standard cable so the charge controller in the laptop is limiting the charge current to 3A so it is only getting 60W.
Quick Charge (QC)
QC2 supports 5V, 9V, 12V, and 20V with a 2A current limit and 18W maximum power. The 20V output is therefore of little use.
QC3 allows the voltage to be chosen between 3.6V and 20V in 200mV steps. If it is provided over a USB-C interface then the current can also be increased to 3A.
QC4 is basically backwards compatible with PD and keeps the adjustable voltages of QC3 so in that regard is very similar to the PPS extension however when falling back to PD it only supports up to 27W. When operating in QC4 mode it supports up to 100W and has slight differences to PD such as the ability to detect the quality of the USB cable and adjust the charging rate accordingly.
Testers
There are many types of USB tester which generally fall into 3 categories.
1) Very basic ones with simple voltage, current and accumulated charge display. The Uni-T UT658 is a good example of one of these.
2) A more advanced one often with a colour TFT display which is also capable of identifying the PD and QC protocol being used and can graph the current. They can often have a bluetooth interface and an app available on a mobile device. A company called RuiDeng make a lot of these with common models being the TC64 and UM25.
Finally models like the FINRSI FNB48 and the Qway Web-U2 (and it's clone the T18-X6). The FNB48 has a bluetooth option but they all have useful extra features that enable them to probe the supply they are connected to and display all the fast charge standards they are capable of, measure a cables resistance, and automatically read the E-marker chip to find the cables capability and detect the presence of an Apple MFI chip.
I have a T18 on order. As an example this is a picture of it's supply detection mode.