Suppose your ADC value measures a voltage. This voltage is related to an exponential decay due to a capacitor discharging and you are using the rate of decay to measure a capacitance. The capacitance is related to the compression of some substance, which is what you want to control. That compression is your "process variable."
To get from the ADC values to the process variable you have to write code that gathers some set of ADC measurements and then takes the logarithm of those ADC values (to avoid a more complicated exponential fit algorithm and to instead use a least squares linear fit, which is easy to find and use -- though it is MUCH better if you have the math skills to deal with the partial differentials needed to develop it on your own whenever you need to.) But before you do that you find you need to remove the ADC offset first. So you do that (using some reasonable means.) You may also have to deal with the gain of the system, but let's say you are only interested in the slope so you can avoid that part.
So now you take the log of the curve, apply a least squares fit algorithm, and work out the slope of the curve as the \$\tau\$. Now, you have something you can use to work out the capacitance, plus some other value which perhaps represents an uncertainty (if you care to do that.)
Now you look up the \$\tau\$ in a table that skips worrying about the capacitance itself and goes directly to the compression figure, which is your process variable.
This process variable can be formatted internally in any way you wish. A lot of people immediately turn it into a floating point value for PID. I almost never do that. But that's a separate story related to applying proper numerical methods techniques and I'm going to avoid it here.
Wow! You have the process variable now. Finally, you can compute your error term and do a step of the PID.
Of course, once you do that you will have a new PID output value. Depending upon the units (dimensional analysis is something you should definitely know cold here), there will be yet another mapping from this PID output value to what you are controlling. And the process for doing that could be as complex as what I just wrote about above. Or worse. Or easier.
There is no simple answer to your question. The above illustrates some of the difficulties. There is a process for conditioning your input(s) in order to arrive at a single process variable measurement. Then you can apply the PID and get a single output from the PID. Then there is another process that takes this output and yet again conditions it in order to generate output(s) from that to control something.
If you do it well, there will be an exact and unvarying time delay between measurements needed to generate a process variable value and the control outputs needed to respond. What makes a PID very frustrating to apply by an operator (and nearly worthless, as a result) are two things: (1) long delays; and, (2) varying delays. Tolerate neither of these, beyond what is absolutely required by the physics and electronic systems.