Typically a borehole is drilled by machine and is relatively small in diameter.
A well is usually sunk by hand and is relatively large in diameter.
Boreholes vs Water Wells
What is the difference between a well and a borehole?; Originally wells were sunk by hand using bricks or rocks as the well liner. The bricks were sunk by their own weight, the bricks were added from the surface and the well sinker would excavate undermining the well walls, hence the term well sinker. This was an extremely arduous and dangerous task and as the sinking was in progress candles were used to test the air for possible leakage of gas/foul air and as a means of illumination. Believe it or not we still used candles up to approximately 20 years ago. Nowadays we are fortunate to have electronic gas detectors.
Today if we are sinking a new well, we would not use bricks but instead concrete rings, although still an arduous task it is considerably faster and safer.
Many years ago boreholes would have been bored by percussion method which would entail driving down the steel liner. This method is still used today, as well as rotary drilling. More often than not the bores are lined with PVC. Sections of the borehole can be left unlined if the formation is self-supporting, for example in sandstone or chalk.
The main advantage of a borehole is that it is possible to penetrate the aquifer to a greater depth ensuring a reliable supply in times of drought or high usage.