Firstly, rain water and tap water taste different from one anopther. If you were taste them yourself, you'd notice the difference.
Secondly, the pH level isoften fairly different. Here locally tap water is fairly neutral ph of 7.0, wheras rain water is fairly acidic say 6.0-6.5.
Thirdly, the mineral or hardness vs softeness is different. Rainwater might have more calcium and trace minerals than tap water.
Forthly, bacteria and live organisms may exist in rain water. Not to mention the chlorine and other chems added to your tap water (unless you've dechlorinated it).