I suggest using "counters", for three reasons:
It isn't redundant. The "-words" part of the alternative is not necessary and is rather unhelpful. Counters are more specific than words, so I suggest we cut out the "word" part, which can be implied by the "counter" part, and keep the tag names as simple as possible.
"Counter" is what most people know it as. I suppose some people do use "counter word" in speech, but I think it's much more common to use plain "counter". I see questions like "what's the counter for chairs?" much more frequently than with the extra "word" after counter. Even though "counter-word" is understandable, I think it's best to keep it as what people use.
Counters is plural rather than singular. This might sound like a weird reason, and maybe I have a misunderstanding of the system. But whenever you type in a tag search field, it always finds a tag name containing the exact string you input, and nothing less. That means that if you type in singular "counter", both "counters" and "counter-words" will appear, but if you type in plural "counters", it will find only "counters", since the extra S doesn't appear in the other one. I'm not sure if this is really a big deal or not, but I thought I should point it out.
As for the description, I think we should, at the minimum, use the current counter-words description, and possibly append the counters description at the end of it. As it currently stands, the counters description on its own provides almost no information about counters.