Distillation of liquids can happen at different temperatures and pressures. For example if we boil water in a kettle at sea level and cool the resultant steam it turns back into water and leaves most of the impurities such as minerals , microbes and bacteria (now mostly dead) in the kettle. If you boil the kettle on top of everest ie at low atmospheric pressure the water boils at low temperature. This is the principle an evaporator works on,Microbes and bacteria are not killed and more pass over to the steam side and collect in the so called distilled water where they multiply more rapidly. Water vapour comes off the surface of water in significant amounts before water boils or our clothes wouldn't dry on the washing line. When this vapour comes in contact with a relatively cool surface it condenses back to water. This is how a condensing dryer works. Few minerals but plenty bugs! Similarly the water collected from an air conditioning plant is condensed with again few minerals but plenty bugs.
From experience, using water collected from driers and air conditioning plants to flush fresh water toilets on tug deliveries, in order to extend our fresh water endurance, I can say that the water collected turns foul in 2 or 3 days and the practice ceased soon after. I might add that one of those bugs is legionella which is deadly.
Boiling water at higher pressures, condensing the steam, sterilising with ultra violet light and chlorinating will give you good potable water but not good for boilers unless the chlorine is evaporated.
Every person who makes a boiler states that we should use "distilled water" and not use "deionised water". Why wouldn't they? It is the only reasonable choice to stop guarantee claims. As you can see from many other threads on this forum this is not as simple as it looks. If you want to be "sure" use the distilled water used to top up lead acid batteries. You can buy it in 10 gallon platic drums. It's not cheap though. If you live in Liverpool or have similar water supply then I can tell you that they (and I) have been putting tap water into their car batteries for Yonks with no Ill effects. Do you have to de-furr your kettle and replace your immersion heater every year cos of calcium build up as people do in certain areas in Cheshire? If so tap water may not be your best choice. But if you have water so soft that it takes ages to get the soap off you in the shower then you can use this type of water. Read BernhardBB's posts on steam, he has been using lake water direct for years with no ill effects. It depends on your lake. I use the lake at Llanberis with no problems.