How did you arrive at this conclusion???
A shotgun is designed as an offensive killing weapon whether its aimed at a person or a pheasant - just because you chose to aim it at a clay pigeon does nothing to reduce its lethality or true purpose.
A BB gun is designed as a recreational amusement, it's not a tool nor a weapon designed for any form of lethality.
This does not mean I don't recognise that in the wrong hands it is capable of causing a severe injury or even a potential death in extreme cases...but then again so is a rubber inner tube at the beach!
People may object to term 'plaything' (and in truth I was being a little controversial) - but it is it's real nature.
The law may define it as a weapon, but surely we can agree it has not been designed as such.