Ok, somebody please explain.

Skynet was a defense system, or program, design to protect america from evil or whatever, then came this virus that was attacking everything it reach and they couldn't stop it because it kept changing. Finally, the goverment decides to activate Skynet for the first time to locate and destroy this virus and when they do all hell breaks loose. The thing that threw me was that then John Connor says that Skynet IS the virus.

So my question is this.
Is this true, is Skynet both the program AND the virus?, if it's so, then how did it spread through the internet if the program wasn't active?

And another thing, even if we accept, ok, it spread... somehow to get people to activate Skynet, why did it attack us? In T2 we learned that the humans turned Skynet on, it became selfaware and when the humans found this as a threat and tried to shut it down, THEN it attacked, so how come in T3 Skynet attacks just because we turn it on?

Thanks for the patience on the reading, I'd really like to hear some other POVs on this.