Tryin to go ta college

Guys I'm confused.  When I look at various college websites, I see programs such as:
Computer Programming
Computer Science
Computer Engineering
Computer Science and Engineering
Computer Science and Engineering Technology
Computer Engineering Technology

That shit confuses me.  You'd think the difference between "Computer Science and Engineering" and "Computer Science and Engineering Technology" would be minute, but they're like totally different programs.  The former seems to be mostly just raw science and includes classes like chemistry, and the latter seems to be a lot of programming classes and - if I had to guess - is easier to complete considering calculus doesn't come up until later semesters.

I want to have a deep knowledge of computers and I want to program shit, and I don't want to be pigeonholed into a single profession for the rest of my life.  Spring semester is comin like what and I don't know what program I'm trying to be in.  Please help me out here.


In before pessimistic and cynical posts about how I'm fucked no matter what.

Based on the answers, it seems like I should do Computer Science and learn random programming languages of goodness on da side.  I do not like messing around with wires and I've never fucked with any form of calculus so I have no idea how much I would like it.  On the other hand for some gay reason I enjoy math.

My question is that it seems like Computer Engineering and Computer Science both offer a deep technical knowledge, but is one in any way superior to the other?  I guess that I want to know how computers tick, so that when I'm programming I have a decent idea of what's going on behind the scenes.  Computer Engineering sounds more boring, but I'd go through the trouble of learning it if it were necessary to do so.