It may seem like a minor detail but there's a very substantial functional difference between "rifles" and "assault rifles": assault rifles can fire as fully-automatic "machine guns".
There is no such thing as "recreational assault rifle ownership". I posted in detail about this in another comment [1], but "assault rifles" are machine guns and are highly regulated in the United States. You can't buy or own one without a special federal permit from the ATF which has a high bar to get. You also can't buy any gun under normal circumstances without an FBI background check.
What everybody is talking about when they say "assault rifle" are actually just "rifles", which function the same way as other hunting rifles and handguns, merely having a different form-factor. AR-15s (ArmaLite Rifles) for example are just normal rifles, not assault rifles. There are many variants, but plenty of AR-15s will fire the same 9mm ammunition that handguns fire. (Caliber has nothing to do with the classification; that's just an example.)
I'm not even sure that individual people can legally possess machine guns in the US. From what I recall you essentially need to form a corporation and apply for it to become a firearms dealer, and get approved; and then the corporation may buy and possess them. The ATF probably tracks every legally sold and owned machine gun in the US. There is very limited "recreational" use of machine guns: you can go to Las Vegas and pay to fire a machine gun that's mounted to the ground, and whose firing angle is limited. That's about the extent to which any normal person (civilian) will ever legally interact with a machine gun or assault rifle in the USA.
For those who want to use informed language to have a precise discussion, please use the term "rifle" if that's what you mean, and avoid using the FUD term "assault rifle" (unless that's what you mean), usage of which has been polluted by poor journalists and opinion-providers that use sloppy language (and an expired law that
skissane points out below).
[1] https://news.ycombinator.com/item?id=26826847