I like to think of water conditioner as something like Rift Lake conditioner or Livebearer conditioner that adds mineral salts to the water to increase GH, KH & pH. These usually (but not always) have a dechlorinator in them.
A dechlorinator is used to neutralise chlorine in tap water. It also breaks the chloramine bond and neutralises the resultant chlorine, leaving the ammonia in the water. Some brands of dechlorinator will also convert the free ammonia into ammonium, which is less harmful to fish. This allows the filter bacteria and live plants to use the ammonium in the treated tap water but the ammonium doesn't harm the fish.
Having said this, in general use and if you talk to most people, they regularly interchange the two words and consider them the same thing.