Is the 'sweat' on the side of bottles distilled water? Are the water droplets that form on the side of water bottles (or other drink containers) distilled water? Assume that the sides of the container are completely clean.
Yes, here is the definition for distilled. 


purify (a liquid) by vaporizing it, then condensing it by cooling
the vapor, and collecting the resulting liquid.


The sweat on the water bottle is the process of distillation, but only the condensation part of the process is seen on the water bottle.