What are good words for "stacking" and "non-stacking"?

Solution 1:

First, although you do not say what you want these words for (adjectives to describe the tags for your "How to Play" instructions? As the names of the 2 kinds of tags?) I assume you mean the latter since you have pretty clearly already described your tags without finding those elusive words.

Second, I don't think the names for your 2 kinds of tags need to be explanatory at all. You explained it well enough to us, and I'm sure you can do as well in your game instructions. That done, you can do what you've done here: just call them Type A and Type B or some other arbitrary contrasting labels, like Blue and Red or Teapot and Turnip.

But, if you think you need descriptive tags, I suggest these contrasts:

Type A/Type B
Pinpoint/General
Bullseye/Net
Special/General
Unique/Generic
Diva/Glee Club

Best of luck with your game.