I think it's a silly distinction to make. Native applications (meaning software running on a computer, outside a browser sandbox) have always offered a smoother, more comprehensive user experience.
That doesn't mean users get no value from the web, or that they're so spoiled by fast transitions in Microsoft Word that they won't want to use a website.
The point is that some -- perhaps many -- people want to distinguish between smartphone apps and traditional programs, and that's one way to do it.
It would be nice if there was a better way, but I don't know of one.
Incidentally, it's a distinction that people also make between "universal apps" (written for Windows Runtime) and desktop programs (written to the Win32 API) even when they do the same job on the same Windows 8 or Windows 10 PC.
The meaningful difference is whether there are isolation and distribution/update mechanisms so that users can install and maintain apps with less risk and hassle. This doesn't have much to do with (in-app) UI per se, though.
It's a broadbrush description but almost everybody gets it.
Would you like to offer a simpler, shorter and more accurate way of making this distinction?