Generally speaking, vacuum is measured against the surrounding atmosphere. We call this gauge pressure, and when it goes negative, that means that the pressure inside the chamber is lower than the pressure of the atmosphere around it.
Thus, for example, a vacuum chamber might have a gauge pressure of -95 kilopascals, meaning that its pressure is 95 kilopascals below that of the surrounding air. This does not mean that the chamber literally has a negative pressure; it actually has a positive pressure inside of perhaps 10 kilopascals, but this is less than the outside air pressure of 105 kilopascals, and thus the net effect of pressure is to compress the chamber rather than expand it.
We could alternatively say that it has a vacuum pressure of 95 kilopascals, where vacuum pressure is simply the opposite of gauge pressure so that we can remove the minus sign.
Theoretically perfectly empty space should have an absolute pressure of 0, so its vacuum pressure would equal to atmospheric pressure, but in the real world we never actually encounter such perfectly empty space; even in deep space there is still a little bit of pressure from ambient hydrogen.
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