Why do I get more channels than I subscribed (time warner)?

I am totally confused with my cable service and what channels I am getting. Help!

This is what I have:

Time Warner Basic Cable Service $10 + $25

What I am getting:

Basic cable channels like the first 30 channels.

With my Digital Plasma TV I am able to get lots of other channels like Golf, TNT, TBS, Oxygen, MTV, VH1, TLC, A&E, FX, etc. etc.

I'm not complaining because I love watching all these channels but I am confused. When I did call Time Warner (carefully!) they told me that if I am getting more channels than the 30 I am picking up channels that are being aired by the state (I didn't get it but I didnt want to keep asking time warner).

My question is:

1. why I am getting more channels than I am paying from Time Warner.

2. if I cancel my time warner basic cable, can I still get all of these digital channels?

If anyone knows what is going on let me know.

Oh and I only get these awesome channels only on my plasma and not my old TV (I assume because i need to get a digital converter for that). My TV is also set to cable and not AIR. When I do change it to air, I do get some channels that i dont get from Time Warner. Actually get like 60 channels but most are asian and spanish channels.