internet vs Internet
To most everyone, "internet" is a thing, not a title.
In this sense, "Internet" is a proper noun, used to refer to one thing rather than a general class of things, and proper nouns are generally capitalized.
I've always understood it to be that Internet = global network, and intranet = local network.
"Internet," without the capitalization, is also a common noun. It is short for "internetwork," which means a network of intranets. What we now call the Internet is an internetwork and used to be called "ARPAnet."