Water Science is a black art but some basics.
Domestic Filtration will take out some nasties including some tastes and taints but not generally minerals or TDS. So DON'T use it on batteries, the minerals and remaining chemicals will react with the acids and plate chemistry.
R/O or reverse osmosis will remove a lot more of the TDS, minerals and tiny particulates and these are generally preceeded by filtration similar to domestic filtration. Depending on the source water R/O can be to pure to drink and is actually re mineralised and ph corrected for human consumption in some cases. R/O will get you between 10-100 ppm on even the worst water. Potentially usable in batteries but a little more post treatment would be in order generally.
De Min or De Ionised waters are nearly pure to under a couple of PPM maximum and a lot lower for lab water supplies. It can corrode stainless steel and destroys copper and some brasses very quickly as well. This is the stuff that goes in batteries and not into humans
50PPM for making Espresso Coffee
100-200 for making Brewed Coffee, Beer or Tea (if you really must).