Squirrel is right. The reason they can go on either is that you position the trv in the best location for air flow. For example, if one side of the rad is behind a couch, press etc. and the other is exposed, put the trv on the side that is exposed. Also, in a room where the rad may be subject to sunlight, e.g. a hallway, put the trv on the side not/least exposed to sunlight.
Also, the bi-directional part is to allow you to position the trv's horizontal or vertical, or parallel with the wall as opposed to perpendicular to the wall where the pipework comes out from the wall. You always want the trv to be horizontal and parallel to the wall where possible. The only time you might have it vertical is where the rad is too close to a door and the trv would actually stop the door from closing if horizontal. Came across this once when I was changing the valves in a small bathroom.
Kevin