In addition to what Peter said, we humans typically use differing terminology to identify function rather than to define something.
If you wanted to go with the raw definition, every network in the world is a small internet, and every internet/intranet is a LAN/WAN just composing of different rules and some variations in the protocols, usually to combat security issues.
However, if you look at the terminology as a term describing function, as in the term defines its purpose rather than defining its fundamental nature, then it's easier to understand. Intranet is a LAN between computers who's function is to be utilized as a local internet. The protocols will almost assuredly be different than a normal LAN/WAN because a normal LAN/WAN is typically meant to severely restrict communications between computers on the network, whereas an intranet would want to be able to do everything the internet does in communications between computers.
It's like when you call a child a toddler or a fetus. The fundamental nature of the object is still the same, but the terminology describes the function. As a fetus, the child is developing through the in-womb stages, as a toddler, the child is developing through the stages of barely learning to walk, focus, and understand speech as well as form words in a rudimentary fashion. (Yes, I intentionally chose this example because both, it's valid and demonstrates a point that perhaps might save someone's life.)
The protocols will be much more complex for an intranet because it has to focus both on allowing connectivity in every feasible way that the internet does, plus prevent unwarranted remote access.
You can find some information here: http://superuser.com/questions/135164/whats-the-difference-between-intranet-extranet-and-internet
– MC10 – 2015-08-15T19:07:34.867