What chemicals cause the softer, less-raw taste of purified water sold in bottles? I've seen the post, "What defines an element's taste?", but it doesn't answer my question.  

I took water that is supplied by the municipality corporation and put it through a gravity based water filter. The taste of the water didn't change. It still had a raw, tap-water kind of taste.  

However, if I buy one of the 20-liter cans (they charge x+y for the water+can and when you return the empty can, they return y amount of money), the water tastes softer and less tap water-ish.  

A 2-liter bottle of mineral water costs x. Which is the same as the 20 liter can cost. So I'm wondering if they really purify it or whether they just add a few chemicals to it to fool people into thinking the water is purified. They might just be supplying us with ordinary tap water or borewell water.    

Are there any chemicals that can change the raw taste of water? Maybe the raw taste caused by chlorine.
Water issues tend to be very specific to a certain location, so it is not possible to say exactly for sure what is happening in your situation.

Pure water has no taste.  The taste comes from the impurities.  Impurities, which are almost always present, can partially be removed by the filter shown.  That filter looks like a carbon filter which is effective on chlorine, organic particles, and sediment.  This filter is ineffective on minerals and inorganic compounds.  

Minerals give tap water its hard taste. This hard taste is harmless (and may actually serve as a dietary mineral supplement.) Removing the hard taste requires a process like deionization or distillation which is costly. The cost of the water can go up significantly with more mineral removal.

Chlorine, which is used to kill pathogens, can be neutralized with citric acid.  Squeezing a lemon or lime in the water can cut down on a chlorine taste.  

Hard water can be chemically softened with something like baking soda; however, this is generally trading one ion for another, so the water will only taste softer. 

Try adding a reverse-osmosis filter after the filter shown. The filter shown will treat the chlorine while the reverse-osmosis filter can treat the minerals. (Chlorine may damage a reverse osmosis filter, so it is best to get it out first.)