Units that can only move in Water terrain probably do not take a penalty to movement in water, while units that can move on the ground probably do. (Rarely can something move as fast on water as it does on land.) Air units do not move through water terrain, they fly over it, and so would not normally take a penalty for moving through a different medium.
Water capable units may be split into two further sub categories. Those capable of travelling only on the surface and those capable of travelling underwater or diving. This may be the case, with the existence of Submarine units.
Some water capable units may be only capable of travelling on the water's surface where they could be susceptible to ranged attacks from shores within the Hex or from Flying units ranged and melee attacks. This would also make them more visible to units entering the hex and possibly leave them unable to attack units capable of travelling beneath the surface of the water, provided those units did not surface within the hex.
Some water capable units are able to travel beneath the surface of the water as well as on it. In some cases, they may be restricted to only making dives to look beneath the surface or directly attack a submerged unit beneath them, in other cases they may be fully capable of remaining and travelling beneath the surface for fixed periods or even indefinately. It is likely that they would be afforded some protection from ranged attacks beneath the surface, be immune to melee attack from Flying units and even capable of avoiding detection from those travelling across or above the water's surface.