What is the difference between hydrostatic pressure and atmospheric pressure?
Here's my explanation.
Both water and air and water are fluids — they can flow from one place to another.
The difference is that water is an incompressible fluid — its density is almost constant as the pressure changes — while air is a compressible fluid — its density changes with pressure.
Hydrostatic pressure is the pressure exerted by an incompressible fluid (a liquid) at a given point, due to the weight of the fluid above it.
Atmospheric pressure is the pressure exerted on a surface by the weight of the atmosphere (a compressible fluid) above it.
The atmospheric pressure at the surface of the earth is approximately 1 bar.
A mercury barometer works because the hydrostatic pressure of the mercury column balances the atmospheric pressure exerted on the surface of the mercury.