glothex,
Full of water means that the height of water column is acting like internal pressure on the wall and bottom junction, (P= rho x g x H = Water density kg/m3 x 9.81 m/s2 x H meters of water height). In addition, the vessel or tank may have some vapour or other gas pressure above the liquid, in which case is called "vapour space pressure" and has to be added to the "Full of Water" pressure, to establish the wall thickness calculation pressure / design pressure. If there is no additional "vapour pressure", that means the vessel or tank is vented to the atmosphere and then you call it "Atmospheric". However, the design pressure is still not zero, but water column only, without additional vapour pressure.
Cheers,