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A router is a router because the vendor so labels it and a L3 switch is a L3 switch because the vendor so labels it. 
As Jon also notes, L3 switches generally have more hardware dedicated to packet forwarding (often very Ethernet only oriented) while routers usually have a much richer feature set and/or media support, but the line is blurred.
I've worked with some vendor X equipment labeled SSR (for smart switch router), so even vendors can blur the line.
Years ago, the 6500 and 7600 could use not only the same sups and some of the same line cards, they ran the same IOS image! However the 6500 was a "L3 switch" and the 7600 was a "router". The did differ, as the 6500 supported service modules that the 7600 didn't, while the 7600 supported special WAN cards that the 6500 didn't. Personally, I suspected the difference was more due to vendor marketing then what could be done technically.
