When you compare capacitors with discharge tubes, you are comparing those vacuum capacitors sealed in glass tubes with gas discharge tubes. There are many other types of capacitors that do not look like discharge tubes thus are not comparable.
Of course the gas pressure and type in the tubes play a big role. In a vacuum capacitor, the residual gas pressure is very low. Thus such capacitors have very high voltage rating and very low loss. Gas discharge tubes, on the other hand, has certain gas pressure left. The amount of gas pressure is intentionally controlled such that at certain voltage the gas can electrically breakdown and becomes conductive. The breakdown voltage is a function of gas pressure and the structure of the tube and is often used as voltage reference devices in old electric equipment.
In a capacitor you do not want the medium between plates to be conductive. In a vacuum capacitor there is almost no gas left in the gap between plates (or between a plate and a pole or between two poles) thus it is not conductive. In an air capacitor (like the one used on old radio to tune frequency), you do not apply voltage higher than the air breakdown threshold thus air is not conductive. In an oil capacitor you have certain voltage limit too. But in a gas discharge tube, you need to keep a low pressure of gas in the tube so that it can breakdown as designed (to be continued)
So even a vacuum capacitor and a gas discharge tube may look similar, they work in different ways. In the former you do not want the medium to break down. In the later you want that, so you design gas type and pressure so that gas can breakdown as you want. With low (but not vacuum) pressure, gas is relatively easier to breakdown because the acceleration length of an electron is long so it gains enough energy to breakdown other molecules on its way. It is called the avalanche effect.