Yes, because "assault weapons" is a made up term that includes large numbers of perfectly legal semi-automatic firearms. The same rifle can have two different configurations, depending on cosmetic variations which do not affect its underlying capabilities, one of which is "scary" looking enough to trigger the "assault weapon" label, while the other appears to be an innocuous hunting or target-shooting rifle.
If by "US law" you mean "federal law," no it does not. It has a legal definition in some US states but they all differ[0] and in every case rely in part of cosmetic features of the weapon.
And I'm not sure what the physical size of a weapon has to do with anything.
