Since there can't be a "remake" of what never existed in the first place, then I honestly don't know what to call it.
But it's not really far off to call it a remake.
I think the best way to classify it as an adaption than a remake. It's adapted from the original Falcom Ys IV script and takes bits from all three versions. So really it's not a remake but more of an adaption.
Now that I played most of Ys Celceta, although I'm late to say what I will, I take back my definition of YsC from before (that it was a "remake of a game Falcom never made + elements from all 3 Ys IVs"), and I'd like to also state that I do agree an "adaption" is the best word to define YsC, BUT! In my humble opinion, for different reasons (warning: long argumentation incoming, read at own risk! ;P):
YsC is an adaption of "Ys IV: Mask of the Sun", "Ys IV: The Dawn of Ys" and "Ys IV: Mask of the Sun -a new theory-" elements put into a completely re-imagined game, extremely adapted to please the current "mainstream" Japanese market.
In other words, I'm trying to emphasize Falcom did not use
anything from their original '93 script that wasn't already there in one of those 3 titles mentioned above, and that anything new we see on YsC was completely made up from scratch just recently (2011/2012). (Most likely anyway, since, y'know, I can't say anything with
absolute certainty as I'm not part of Falcom's staff.)
Now, regarding what I just said, I'd like to clear and highlight some points:
Falcom has
always tried to appeal successfully to the Japanese market in a way or another, so naturally their outdated, original '93 script probably wouldn't work as well as YsC in sales (and that too if they even have it, and it has not been lost or left along with their old employees).
Making money is not much of a problem, but! Part of the marketing they used is, IMO, because it's misleading: "Fans have always asked us we make our own in-house Ys IV. So, YsC is our answer to our fan calls." What fans really wanted was the supposed REAL Ys IV, which we, fans, believed would only exist if Falcom themselves made it directly, and not through a 3rd party. But YsC is not that: Storywise, it's a completely new game (which is not what those fans wanted), but marketed as THEIR take on Ys IV, even though it's not. It's a complete
re-imagining of Ys IV's story focused on pleasing today's masses, and that too with heavy influences from said third-party-developed 3 Ys IVs.
I think it's also noteworthy that the game's real name, "Ys: The Sea of Trees of Celceta" (well, "Celceta no Jukai") is a nod to how Falcom marketed the game to be the "real" Ys IV story (even though they purposefully did not put "IV" in the name), since "Celceta no Jukai" was the name of Adol's adventure in Celceta mentioned in the pre-story found in the manual of Ys I for most JP home computers (PC-88, FM-7 etc.), and perhaps it was there in Ys ETERNAL's loading screen, too. That makes it feel like they are saying "this is THE take on Ys IV's story".
So, going back to the real question ("Do we call this a remake? An adaption? A new game? Falcom's Ys IV?"), I think the most false way to describe this game is to call it "Falcom's long-planned Ys IV". Shamefully, the otherwise amazing website, "Ys Music Files", even erroneously put the "IV" in its name and called it "Ys4: Celceta no Jukai". And that's sadly how quite a few other, particularly newer fans think it is, too.
Similarly, though, calling it a "remake" isn't accurate either, because Falcom never made Ys IV in the first place, but it IS less wrong, simply because it
does act as a remake of the other 3 Ys IVs. A remake of games made by other companies. But since that's not 100% what YsC is, that's also not right.
So, either an "adaption" or a "re-imagining" it is.
Well, that's all the randomness I had to say on this matter.
Maybe a bit pointless, but valid I presume, nonetheless. As long as we still care.
Also, hopefully no one will take this offensively: all Falcom criticism here is meant to be constructive, and in advance I apologize if anything here is taken the wrong way! Just wanted to share thoughts on this, really.