Pressure inside water vs. atmospheric pressure

For a non-moving body of water the pressure at the surface is the atmospheric pressure, and "inside" the water the pressure increases with depth due to the weight of the overlying water. You can look up the relationship in any basic physics text.

For water that is moving, it is more complicated; see a thermodynamics text.

Reponse to your comment. For a capillary tube with one end in a pan of water, the level of water inside the small tube is higher than the level of water in the pan due to surface tension effects inside the small tube. Water rises up into the tube till the total upward force due to surface tension is equal to the downward weight of water inside the tube. At the water/air surface at the top of the tube the pressure is the atmospheric pressure and at the water/air surface in the pan the pressure is also the atmospheric pressure.

In the water in the tube, at the interface the pressure is lower than the atmospheric pressure. See the following discussion of Jurin's law on Wikipedia: https://en.wikipedia.org/wiki/Jurin%27s_law

Search the web for capillary physics for more details.