Confusion with T1 vs. Cable speeds.  Looking for some explanation please...

I've never really had the chance to play with any high speed connection other than my RoadRunner (5Mbit) at home.  I've recently gotten a new job at which we have a T1 run for our dedicated internet access.

I've always known that T1's are 1.5Mbit, but I never really thought about that?  I was always under the impressions that the order of speeds was: dialup, dsl, cable, t1, t3.  In my mind I've always thought, "wow I wish I could have a T1 to my house."

However, am I accurate on that?  As I said my RoadRunner is 5Mbit and when I run bandwidth tests I do indeed get that.  When I download at home from good servers I get speeds upwards of 600Kb/sec.  Here at work, though, I only get about 180Kb/sec, and now that I do the math, that seems right.  180Kb/sec is roughly the 1.5Mbit that a T1 gets.  

So, is cable actually faster than a T1!?  Why do so many business use T1's and not cable modems if this is the case?

Also, I never really knew this either, that T1's were actually run with phone lines???  The way people explain why cable is faster is by saying something like "a phone cord is only this thick, where-as a coax cable is about 3 times as thick, therefore it's like more lanes of traffic, it can go faster."  But apparently that's not the case.  If a T1 at 1.5Mbit can come in through a phone line why were we stuck with 56kbit connections on dial for so long?  Are these so called high-speed dial up ISP's using technology similar to a T1?

Sorry if I sound like an idiot.  I thought I knew the differences between these connections but I guess I'm wrong.  Anything you can tell me to help me understand would be greatly appreciated.  Thanks!