From what I can tell (based on HN and other forums), systems research is empirical testing of systems, while theoretical computer science is math heavy. The typical systems paper is "The design, implementation, and performance of a [application] system, using [technology]". While a theory paper is "Proof of the existence of a solution for [problem] in time [O(something)]".
These two branches do talk to each other, but not much.
In general you got it, but CS theorists do more than just algorithmic analysis. They also may be after some other desired, provably guaranteed effect with an algorithm, and they'll say in passing "By the way, this is a linear algorithm, so it's performance isnt an issue." This is true in scheduling, cryptography and probably many other areas. (It's early, sorry.)
You got systems research pretty much head-on, but I would stress the design and implementation part more. That is, CS systems research tends towards engineering, where we claim we made a better whatzit, and then we need to provide a suite of experiments to support our claim.
These two branches do talk to each other, but not much.