Difference between Internet (capital I) and internet

Internet with capital 'I' refers to the Internet as in the world wide web, and what most people think of when you say internet.

Internet with a lowercase 'i' refers to a bunch of small LANS connected together to form some kind of host-to-host packet delivery service. So basically Internet capital I refers to inter-networking at the global level. Whereas internet with a lowercase 'i' refers to it on a much smaller level.