Assume liquid is non-volatile

The first picture does not have a lid, but the second one has a lid on the jar.

I am not sure of this, cause I have an explanation for both the type of answers.

 

For 'yes',I have :  Yes cause the amount of air inside the jar is going to be the same and hence the amount of air pushing on the water surface is the same and thus the same pressure! But for 'no' I have to say that when I am closing the jar I am closing it from the atmosphere and hence the amount of air on top of the column changes, and thus the pressure wont be the same! I sound sort of contradicting cause I havent understood this properly.Please help me out!