distilled water vs purified water for batteries

[GringoPhil]

purified water vs. distilled water for the batteries ( coach, and/or starting batteries).

Not looking to save money here, but maybe lazy, saving a trip to the store if I am out of distilled water, and only have purified "spring" (ha ha) water.

Is there some chemical or other property of distilled that lasts better in the batteries? or prolongs their life? Or is the purified bottled water OK as well?

Thank you - Phil