Both can. Every service that runs under the hood (recommenders, raters, story fetching, login, etc.) is an agnostic API that can be used elsewhere. Some of the auto manufacturers and TV apps were already using a scaled down version, albeit without all the features and services of NPR One
These are public NPR API endpoints, most have changed little since their launch in July 2008: http://dev.npr.org/
There are about 2 dozen endpoints that aren't public, either because they have little use outside the building, they may contain sensitive info, or they are valuable but only available with licensing. I'm going to explain NPR's finances a bit more in the above thread.
EDITs: I'll add that off the top of my head, some of the private APIs that power NPR one are used in at least one connected TV app that may not have launched, and also in some car partners. We built a great API on top of NPR's internal library database a few years back. Librarians tag the people, movies, songs, etc. used in every NPR radio story going back decades. That one isn't yet robust enough to handle outside use, but if they release it it's really interesting.
The story API (public, above) is the workhorse. Literally every mobile/car/web app and all stations and other websites syndicating NPR content use that one.
Also, I see no reason both shouldn't exist. Why not make the thing you want?