Hi.
In general it is pretty easy. A social network is a structure build of individuals (or even companies), the so called "nodes" which are connected to some or all of the other members depending on specific profile entries (special knowledge, gender, age....the list is endless).
One social network in its clearest form is XING (www.xing.com) where the connection between two or some persons are build only (well, almost) on business facts, like Mr X is s colleague of me, therefore i am connected also to Mr Z (who knows X), allthough only in the second level.
There is a theory, that every single person on this planet knows every other (!!!) person latest after 7 hops. I haven't found something against this theory by know.
Your second question: social networking is just "doing it" or being part of a social network and making it bigger from time to time, as you meet new people in real life and you will connect to each other on a social network platform.
Third, a website can be called a social network platform when it delivers the funcionality for building social networks.
Hope that helps.
Cheers
Kai