Does Zen distinguish between concentration and insight meditation? Both the Theravada and Tibetan systems distinguish between two aspects of meditation -- concentration (aka shamata, serenity, calm abiding, shiney or zhiney (Tib.)) and insight (aka vipashyana, lhatong (Tib.)). (Some call them types of meditation, but I prefer aspects, since you need your concentration skill while doing insight work -- in fact, that is what concentration is for -- but you can at different times be aiming at one or the other.)

The question -- does Zen make a similar distinction? 

I realize Zen is not monolithic, so answers for specific schools are fine.
I'm far from an expert and even more far from knowing all the technical words, but I sit in Soto tradition.

As @enenalan already mentioned, Soto has a more shamatha approach, called shinkantaza, or just sitting. (@enealan: there is your answer, even if I just acknowledged to not answer another answer ;-) )

The meditation in Soto, at least in the tradition of my lineage, is an aimless meditation. It is not only aimless in terms of no insight, no solving koans, no tinkering with truth and such stuff, but also in terms of not meditating for any benefit. We are not supposed to sit to become better people, get insight, be calmer or whatsoever.

While you are in (Soto-)Meditation, you are supposed to watch or notice [was: examine, see comment] our mind. Therefore there is a component of insight. But we should do so as a spectator, not as a judge. The insight comes naturally, over time, and is a side-effect and not thought to be the goal of the practice.

On the other hand, to stay focused, not to let your thoughts wandering, not to start daydreaming or become sleepy. To watch and not not judge our thoughts, how they emerge and vanish, requires a huge amount of concentration.

As a Conclusion: Soto knows (as far as I am Soto) only on kind of meditation, and that covers the concentration aspect. Insight grows over time naturally and is not active fostered during meditation.