When it is above the water table, in the vadose zone, it is called perched ground water.
river
ground water
A quarry is the name for a place where rock is taken from the ground. It is always above ground. A mine can be below ground or at ground level and is where ore is taken from the ground. Marble is quarried, coal is mined. That is the difference of a mine and a quarry.
Groundwater
The name Waterfall is derived from the place name Waterfall in Staffordshire, England. It's derived from the Old English "wætergefall" meaning "place where a water course disappears below ground".
A volcano erupts
Water that is found under water is GROUND WATER 100% ♥Ü☼
Ground Zero
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The water table
When it is above the water table, in the vadose zone, it is called perched ground water.
uluru
river
They are called groundwater. Far as I know, there is no specific name separating ground water in shallow water table and the ground water in confined aquifer. So you might have to called by the full description "groundwater in confined aquifer layer". Aquifer is the specifics name for porous rock and earth media in the question.
Either Dormant or Extinct
Mount Fuji