I write "Internet". It's not one of a class of things, it is _the_ thing. Similarly I'll capitalize Earth, Moon, Sun, and Solar System when referring to the specific planet humans live on, moon orbiting that planet, the star they both orbit, and the solar system containing them all. But there's also "earth" as in dirt, and generic moons of other planets, and suns of other solar systems.

It's also interesting to note that the Internet is a superclass -- it's a network of networks (you'll discover this if you dig into BGP and realize what ASNs represent). And for networks connected via TCP/IP and BGP, it's the superclass of all such networks and a universal.

If it were to fragment, or one or more independent networks were to emerge, or sufficiently off-planet networks would develop that couldn't directly participate in terrestrial Internet traffic, that's going to remain the case.