After reading your comment, I agree that this is probably just a semantic question with no real meaning. This is interesting, because I completely failed to realize this myself and instead constructed an elaborate rationalization for why the distinction exists.
While reading the wikipedia page, I found myself interpreting meaning into these two viewpoints that were probably never intended to be there. I am mentioning this both because I find it interesting that I reinterpreted both theories to be consistent with my own believes without realizing it, and because I would like to see what others have to say about those reinterpretations. I should point out that I am currently really tired and only skimmed the article, so that probably wouldn't have happened under ordinary circumstances, but I still think that this is interesting because it shows the inferential gap at work:
I am a computationalist, and as such the distinction between the two theories was pretty meaningless to me at first. However, I reinterpreted the two theories in ways that were almost certainly never intended, so that they did make sense to me as a reasonable distinction:
the A theory corresponds to living in a universe where the laws of physics progress like in a simple physical simulation, with a global variable to measure time and rules for how to incrementally get from one state to the next. I assume for the purpose of this theory that quantum-mechanical and relativistic effects that view time non-linearly can be abstracted in some way so that a single, universal time value suffices regardless. I interpreted it like this because I thought the crux of the theory was having a central anchor point for past and future.
the B theory corresponds to living in a highly abstracted simulation where many things are only computed when they become relevant for whatever the focus of the simulation is on. For instance, say the focus is on accurately modelling sapient life, then the exact atomic composition of a random rock is largely irrelevant and is not computed at first. However, when the rock is analyzed by a scientist, this information does become relevant. The simulation now checks what level of detail is required (i.e. how precise the measuring is) and backpropagates causal chains on how the rock came to be, in order to update the information about the rock's structure. In this way, unnecessary computations are avoided. I interpreted it like this because I thought the crux of the theory was the causal structure between events.
In essence, the A theory would correspond to a mindless, brute-force computation, while the B theory implies a deliberate, efficient computation that follows some explicit goal. This is nowhere near what the A and B theory actually seem to say now that I have read the article in more detail. In fact, the philosophical/moral implications are almost reversed under some viewpoints. I find it very interesting that this is the first thing that came to mind when I read it.
I probably should have written "presentism" and "eternalism" instead of "A-theory" and "B-theory". Does the dispute between presentism and eternalism also seem to you to have no real meaning?
I've always been puzzled by why so many people have such strong intuitions about whether the A-theory or the B-theory1 of time is true. [ETA: I've written "A-theory" and "B-theory" as code for "presentism" and "eternalism", but see the first footnote.] It seems like nothing psychologically important turns on this question. And yet, people often have a very strong intuition supporting one theory over the other. Moreover, this intuition seems to be remarkably primitive. That is, whichever theory you prefer, you probably felt an immediate affinity for that conception of time as soon as you started thinking about time at all. The intuition that time is A-theoretic or B-theoretic seems pre-philosophical, whichever intuition you have. This intuition will then shape your subsequent theoretical speculations about time, rather than vice-verse.
Consider, by way of contrast, intuitions about God. People often have a strong pre-theoretical intuition about whether God exists. But it is easy to imagine how someone could form a strong emotional attachment to the existence of God early in life. Can emotional significance explain why people have deeply felt intuitions about time? It seems like the nature of time should be emotionally neutral2.
Now, strong intuitions about emotionally neutral topics aren't so uncommon. For example, we have strong intuitions about how addition behaves for large integers. But usually, it seems, such intuitions are nearly unanimous and can be attributed to our common biological or cultural heritage. Strong disagreeing intuitions about neutral topics seem rarer.
Speaking for myself, the B-theory has always seemed just obviously true. I can't really make coherent sense out of the A-theory. If I had never encountered the A-theory, the idea that time might work like that would not have occurred to me. Nonetheless, at the risk of being rude, I am going to speculate about how A-theorists got that way. (B-theorists, of course, just follow the evidence ;).)
I wonder if the real psycho-philosophical root of the A-theory is the following. If you feel strongly committed to the A-theory, maybe you are being pushed into that position by two conflicting intuitions about your own personal identity.
Intuition 1: On the one hand, you have a notion of personal identity according to which you are just whatever is accessible to your self-awareness right now, plus maybe whatever metaphysical "supporting machinery" allows you to have this kind of self-awareness.
Intuition 2: On the other hand, you feel that you must identify yourself, in some sense, with you-tomorrow. Otherwise, you can give no "rational" account of the particular way in which you care about and feel responsible for this particular tomorrow-person, as opposed to Brittany-Spears-tomorrow, say.
But now you have a problem. It seems that if you take this second intuition seriously, then the first intuition implies that the experiences of you-tomorrow should be accessible to you-now. Obviously, this is not the case. You-tomorrow will have some particular contents of self-awareness, but those contents aren't accessible to you-now. Indeed, entirely different contents completely fill your awareness now — contents which will not be accessible in this direct and immediate way to you-tomorrow.
So, to hold onto both intuitions, you must somehow block the inference made in the previous paragraph. One way to do this is to go through the following sequence:
One potential problem with this psychological explanation is that it doesn't explain the significance of "becoming". Some A-theorists report that a particular basic experience of "becoming" is the immediate reason for their attachment to the A-theory. But the story above doesn't really have anything to do with "becoming", at least not obviously. (This is because I can't make heads or tails of "becoming".)
Second, intuitions about time, even in their primitive pre-reflective state, are intuitions about everything in time. Yet the story above is exclusively about oneself in time. It seems that it would require something more to pass from intuitions about oneself in time to intuitions about how the entire universe is in time.
1 [ETA: In this post, I use the words "A-theory" and "B-theory" as a sloppy shorthand for "presentism" and "eternalism", respectively. The point is that these are theories of ontology ("Does the future exist?"), and not just theories about how we should talk about time. This shouldn't seem like merely a semantic or vacuous dispute unless, as in certain caricatures of logical positivism, you think that the question of whether X exists is always just the question of whether X can be directly experienced.]
2 Some people do seem to be attached to the A-theory because they think that the B-theory takes away their free will by implying that what they will choose is already the case right now. This might explain the emotional significance of the A-theory of time for some people. But many A-theorists are happy to grant, say, that God already knows what they will do. I'm trying to understand those A-theorists who aren't bothered by the implications of the B-theory for free will.