internet vs Internet

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."

So: "Internet" = the global network system whatever "intranet" = local network "internet" = group of intranets