The "assault rifle" has always had a specific definition: a shoulder-fired, selective-fire weapon with a detachable box magazine chambered for an intermediate power cartridge. Civilian semi-automatic "modern sporting rifles" like AR-15s and such look like assault rifles, but don't technically fit the description because they don't have a fully-automatic firing mode.

"Assault weapon" is trickier to pin down, as it's not a term that comes from the gun world. It is instead a term made up in the 1980's, possibly by gun control activists, and popularized by journalists. In use, it seems to refer to any firearm with a military appearance. People familiar with the actual lexicon of gun-related terms don't use it, save perhaps in reference to the term.