Artesian well vs. Water Table well

How can you tell if you have an artesian well that is the non-flowing kind (there are flowing and non-flowing artesian wells), and not just a normal water table well (a well that is not fed by a confined aquifer)?

From a Google search;

An artesian well is a water well that doesn't require a pump to bring water to the surface; this occurs when there is enough pressure in the aquifer.

What's the difference between an artesian well and a flowing artesian well ?
- An artesian well is a well that taps into a confined aquifer.
- A flowing well is under  pressure, causing water to rise above the top of the aquifer where its tapped, but does not necessarily above the land surface .

I am used to seeing the water above and below the confining layer referred to as surface water and ground water respectively. My understanding is that surface water will be more rapidly and dramatically affected by recent rainfall than ground water. This is more apparent with springs, where springs that only flow or flow much harder after recent rains are usually surface water, where springs that flow relatively consistently year round are typically groundwater. The non-flowing artesian well would be more difficult to assess than a spring, but for starters I would check the water level before and after a rainfall event and see if it fluctuated significantly.

The hydraulic response of the well to pumping stress will be different in confined versus unconfined aquifers..
See:  https://pubs.usgs.gov/circ/circ1186/html/boxa.html

You can often tell from the drillers log, if available, or talk to a local drilling contractor or hydrogeologist familiar with your area.

The majority of domestic wells are shallow and completed in unconfined aquifers.