I was inspired by this question, and in particular this section of user259242's answer:
Type identity physicalism says mental states are identical with brain states. Eliminativism on the other hand states that mental states don't exist at all.
Isn't this just a word game? Does it really matter whether we say "Super-Man is identical to Clark Kent" or whether we say "Super-Man doesn't really exist, only Clark Kent does"?
You describe with dazzling precision the exact difference between the two positions. And so you ask a further question (I take it to be the real question): Isn't this a word game?. I suppose that it is, in the same way that the statements "the Earth is round" and "the Earth is flat" differ only as part of a mere 'word-game', if that refers simply to the fact that 'round' and 'flat' are words.
While I understand the point, I'm struggling with the idea that the Superman question is as much a semantic argument as the flat earth. What we mean when we say the earth is round is that it fits a set of criteria, e.g. if you measure the distance between two points, the path along a certain arc is shorter than a straight line. We can define roundness completely in terms of observations you can make about the object in question. However, it doesn't seem possible to observe that something exists. In particular, two people can make the same observations about an object and then proceed to disagree about whether it exists. How could it be that what the two people disagree about is not simply the meaning of the word "exist"?
Consider a question like, "Does Santa Claus exist?" My personal inclination is to be kind of a pluralist, and say that there is some sense in which Santa does not exist, but also a sense in which he does exist (as a fictional character). These two options do not seem to me like metaphysical statements, but rather describing the same situation in two different ways using two different meanings of the word "exist".
If my question seems rambling or it's unclear what I'm asking, it's because I feel profoundly confused on this point.