The main difference is the height to which groundwater rises naturally inside the borehole. Both access a confined aquifer, where water is trapped between relatively impermeable layers and held under pressure.
Artesian Borehole
An artesian borehole penetrates a pressurized confined aquifer. If the hydraulic pressure is strong enough, water rises through the borehole to the ground surface and may discharge naturally without pumping. This is specifically called a flowing artesian borehole.
Sub-Artesian Borehole
A sub-artesian borehole also taps a confined and pressurized aquifer, but the pressure is insufficient to push water all the way to the ground surface. Water rises inside the casing to a level above the top of the aquifer but remains below ground level, so a pump is required.
Key Difference
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Artesian: Water rises to the surface naturally and may flow without pumping.
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Sub-artesian: Water rises naturally inside the borehole but remains below the surface and requires pumping.
The term artesian is sometimes used broadly for both conditions because both boreholes draw water from confined aquifers under pressure. Strictly speaking, a borehole that flows naturally at the surface is a flowing artesian borehole, while one that does not overflow is a sub-artesian or non-flowing artesian borehole.