(Most of this answer is copied from my answer to your other question. This is certainly asking a different question, but much of what I said there applies.)
What are Hit Points, and why do they change?
First, let's make sure we know what hit points actually are.
Hit points represent a combination of physical and mental durability, the will to live, and luck. Creatures with more hit points are more difficult to kill. Those with fewer hit points are more fragile.
A creature’s current hit points (usually just called hit points) can be any number from the creature’s hit point maximum down to 0. This number changes frequently as a creature takes damage or receives healing.
Whenever a creature takes damage, that damage is subtracted from its hit points. The loss of hit points has no effect on a creature’s capabilities until the creature drops to 0 hit points.
It's generally established, though I don't know of a rule that makes it perfectly explicit, that if your maximum hit points becomes lower than your current hit points, that your current points becomes your maximum hit points (See "What happens to current hp upon loss of max hp?".) Since due to the definition of "current hit points" it needs to be within the bounds of 0 to your maximum, and your maximum has changed, it makes sense that it has to change as well. But it'd be real silly if it were to change to, say, 0, or to a random number less than the new maximum. Changing to the closest number that's still within the bounds allowed for current hit points makes the most sense, and nobody would really expect it to work differently.
Does this change to your current hit points count as damage?
Your hit points just "becoming" a number is part of what's a bit odd about all this. As you've noted, it's not clear if there's a way of reducing one's current hit points that isn't called damage.
Arguments in favor of it being damage
Arguments in favor of just being a change in current hit points
- Nothing in the rules calls out this reduction in current hit points due to a reduction in maximum hit points as "damage", and generally game terms are used in a somewhat consistent manner.
- The sentence "Whenever a creature takes damage, that damage is subtracted from its hit points." says that while damage subtracts hit points, it doesn't say that it's the only way to do so.
When describing how damage works,
Different attacks, damaging spells, and other harmful effects deal different types of damage.
None of the types listed seem to apply, as we have "rules damage" or "maximum hp reduced damage", and it's clearly a different sort of thing than the types of damage listed.
You're being non-committal. Which is it?
RAW, it doesn't really say. All of 5th Edition has a philosophy that the rules are really just guidelines to help make your own games. I expect DMs to read it however they find reasonable. Per "Rule 0" (Or, if you want an actual citation, the Introduction's "How to Play" section), the DM determines the environment the players are in and results of the players' actions. "The DM decides what happens, often [but not necessarily] relying on the roll of a die to determine the results of an action."
In practice, for a lot of cases, one gets the most sensible answers from the rules if you apply the same rules that apply to damage being dealt (such as falling unconscious when damage takes you to 0 hit points), even though there's a good argument to be made that it isn't technically damage.
For other cases, such as your example of concentrating on a spell, it would be reasonable for a DM to rule that the loss of hit points wasn't something that would affect one's concentration on a spell. Another DM might rule that in fact they would need that Constitution check, because they do in fact suddenly feel "weaker". Both would be completely correct in doing so (though I'd expect a particular DM to generally be consistent in such rulings).