Anime reviewers refer to “art” and “animation” separately. What does each one refer to?
While I imagine there's variance in how reviewers use words, I would think that most would choose to describe "art" as being still imagery (backgrounds, clothing design, static pans, color choices, etc.) and "animation" as being, well, animated imagery (character animation, CG, combat scenes, sakuga, and so forth).
Is there more to the visuals than the characters and the backgrounds? Conversely, am I oversimplifying it?
Dividing the visuals of an anime into "characters" and "backgrounds" is not all that wrong (though it raises the question of how one ought to characterize things like mechas and non-static background elements). But it's a fairly artificial distinction, and one that isn't too useful as part of a critique of an anime. There are still shots of characters (for example, when the camera pans over a character), and there are animated shots of characters (facial animation, walking motion, etc). Likewise, there are still shots of background details... but some backgrounds are animated, too. Take, for example, this segment from Nichijou.
The distinction between "art" and "animation", on the other hand, is, in some cases, a useful dichotomy: it is frequently the case that the people who do the animation for a show (keyframers, tweeners, and so forth) are different from the people who do static art assets like backgrounds (background artists, 3D modellers, etc.). As such, I think it makes some sense to evaluate the two separately.
It is probably often the case that the perceived "quality" of the art and animation of a given show are fairly well-correlated - a studio that hires or contracts skilled background artists will probably do the same with their keyframers, and a studio that hires bottom-barrel animators will probably hire bottom-barrel painters.
But sometimes, reviewers will observe a marked difference in the quality of the art vs the animation. Consider, as an example, Bakemonogatari (not the whole series; just Bakemonogatari itself). The animation in Bakemonogatari is frequently very limited (or, in the TV airing, absent altogether, replaced by screens of text instead). But the art is often remarkably elaborate.
And going the other way, The Tatami Galaxy has fairly mundane-looking art. But when you see it in motion, you might find that still screencaptures of the show don't suffice to convey how fluidly the show is animated in many of its shots. (The "mundane" art of The Tatami Galaxy is clearly an intentional artistic choice, unlike the limited animation of Bakemonogatari, which probably isn't. I've used it as an example anyway since I can't think of anything better off the top of my head.)
Bundling "art" and "animation" into a single category called, say, "visuals" loses some of the granularity that would allow a reviewer to discuss the ways in which Bakemonogatari succeeds with its art whereas The Tatami Galaxy fails, and vice versa regarding animation. So I guess that might be why critiquers of anime would choose to evaluate "art" and "animation" separately.