Computer science - will teach you theory of computing, computer architecture, algorithms, computer math, etc. You will do some programming, but this degree will teach you about how to solve problems, etc. You teach yourself how to program as needed.
Computer programming - normally not a 4 year program. Generally found in a trade school, technical school, junior college, etc. as a 2 year program. Will teach you programming languages, and maybe some theory, but will focus on real-world, immediately marketable programming skills.
Computer engineering - more hardware focused. Teaches more in-depth processor design, etc. Closer to electrical engineering than computer science. The programming you'll do will likely be in a hardware description language, or a small amount in assembly, or maybe C, to demonstrate the hardware-software interface (the Instruction Set Architectire). This will probably not prepare you much for a programming career, but rather a career in hardware design, validation, verification, optimization, etc.
This isn't formal, just my opinion of what these generally encompass.
If you're seriously interested in a longterm career in software, I'd go CS. I'm biased though, as that's my background.
-Lee
Edit: oops, thought you said computer engineering, not software engineering. I don't have any experience with an SE program. I'm guessing you'll do theory like CS while also focusing on project management, software design techniques, team development techniques, etc. Dependent on the program this may be a better fit than CS, but without specific curricula to review, it's impossible to say.