I have read both FAQs, and it looks like these two SE sites have many things in common. Or, am I mistaken?
CSTheory.SE is for research- and graduate-level questions in theoretical computer science. If you're not a graduate student or a person with a PhD in computer science, the site's not the place you're looking to ask a question.
Programmers.SE is for professional-level, high-level questions in software development and programming. If you're working on a practical problem in a professional setting and trying to figure out some high-level question, this is where you want to be.
For the sake of completeness:
Stack Overflow is for programming questions of all levels that deal with working directly with code: if you want help with code not compiling, specific implementation issues, and other low-level stuff, you'll want to ask there.
There is no site that best serves undergraduate-level computer science questions currently. They're on-topic here and on Stack Overflow, but they do fair-to-middling at best. There is a site proposal currently in the commitment phase for that.