Even in past editions, in the default cosmology, no, but.
In D&D 3e, there is an explicit statement that time flows the same on all planes save the Astral:
Time Along the Great Wheel
Within the D&D cosmology, time flows at a normal rate, and all planes have the normal time trait. Planes with the flowing time trait or the erratic time trait change the game too dramatically for most player’ tastes.
The only exception to this is the Astral Plane, which is a timeless plane for purposes of aging, hunger, thirst, and natural healing.
(Manual of the Planes pg. 10)
The Great Wheel is the default cosmology of D&D, used (by name) in 2e and 3e, but 1e also used a similar (unnamed) cosmology, and 5e seems to as well though we don’t really have a plane-dedicated book. (D&D 4e did something... entirely different, that 5e has mostly ignored aside from the Feywild, and using some of the names of 4e planes as kind of “poetic” names for Great Wheel planes.)
And the preference for normal time seems to be consistent in each of those editions, too: I spoke with a Planescape expert about 2e planes, and none with other planar time traits came to mind for him, and 5e has specific statements about not messing with time, as quoted in other answers.
However, note the reference to “the normal time trait.” That’s because, despite the fact that it didn’t use them, this edition defined other potential time traits for planes, including flowing time,2 defined as
On some planes, time can flow faster or slower. One may travel to another plane, spend a year there, then return to the Material Plane to find that only six seconds have elapsed. Everything on the plane returned to is only a few seconds older. But for that traveler and the items, spells, and effects working on him, that year away was entirely real.
Furthermore, despite the statement in Manual of the Planes, there are (or were) some exceptions that actually used flowing time.3
A slow-time demiplane was apparently possible
Planar Handbook (the Planescape book for the “v.3.5 revised edition” of D&D and a kind of sequel to Manual of the Planes) mentions the possibility of a “planar breach” from a “slow-time demiplane.” That suggests that, despite not appearing in any of the major planes of the Great Wheel, demiplanes (which are often created by spellcasters, usually for their own personal use) can be constructed with flowing time traits.
Eberron—originally, at least
Eberron—whose debut in the “v.3.5 revised edition” made no mention of the Great Wheel and no attempt to be compatible with it—had moons that were also planes, somehow, and they had planar traits including some different time traits:
- Dal Quor, the Region of Dreams: flowing time, ⅒×Material
- Dolurrh, the Realm of the Dead: timeless
- Thelanis, the Faerie Court: flowing time, 7×Material
- Xoriat, the Realm of Madness: “distorted” time, 60×Material (no idea why this wasn’t just flowing)
However, Eberron: Rising from the Last War says that the moons are just moons, and not planes, and makes no mention of differing time scales. It is unclear if this means they no longer have them or not, nor is anything about this ret-con explained in any manner. There are a lot of very serious problems with this ret-con,4 even ignoring older edition material,5 so I view the whole matter with a lot of skepticism.
The exceptionally-timeless nature of the Astral has more significant repercussions than mentioned here, by the way—for one thing, that fact is why teleportation works, because you travel some distance in the Astral and pop out somewhere else in the Material, and the transit time is 0 from the Material’s perspective because time doesn’t move in the Astral. This property is... insufficiently defined to bear very much scrutiny, however. Taken literally, you would think the Astral would be very crowded with every teleportation performed by every creature to ever exist.
The other time traits are the aforementioned normal, timeless for the Astral, and erratic time, where the plane is inconsistently faster or slower.
None seem to have used erratic time, and frankly I have no idea how you would run such a thing. I guess do something similar to what the Feywild does, but 3e didn’t provide a table as the 5e DMG does.
The issues are not primarily to do with the moons themselves, and whether or not they are planes, but rather with the connection of Eberron to the Great Wheel/wider multiverse. A ton of the tension in Eberron stems from being stuck with their own cosmology, and not being able to interact with other planes. No one in Eberron even knows if gods exist at all, much less can confirm their beliefs per se; in the Great Wheel, it’s not terribly hard to go meet a god in person. Likewise, in Eberron, almost everyone is consigned to Dolurrh on death, to be recycled—this is a major impetus for faith in at least two major religions, the Silver Flame and the Blood of Vol. In the Great Wheel, (almost) everyone just goes to their own deity’s divine realm. Adding Eberron to the Great Wheel is not impossible, but there needs to be some kind of explanation why the other planes haven’t completely upended Khorvairan society, maybe something like the Gray of Athas. Eberron: Rising from the Last War did not provide one.
Which itself is a mistake since 5e has one book about Eberron while 3.5e had over a dozen and that’s not counting adventures.