There is an interesting case of two "editions" remaining in print without changes to the setting...
Let's look at Pendragon:
1st Edition was version 1 of the mechanics.
2nd Edition (when they counted to label 3rd ed) was a reprint of 1st ed, so version 1
3rd edition was a slight revision of mechanics, a rather important change to character gen, and integration of some 1e supplement options. So, Version 2.
4th edition was an expansion of 3rd ed, with minor economics changes, and incorporating all but one table of the supplement Knights Adventurous, so essentially version 2.1. 3rd ed was still in distribution.
4½ ed was a small but potent change in Character Generation and expands combat options, but the released core, Book of Knights, lacks the non-CGen, non-combat, non-advancement mechanics. Essentially, a player's handbook to 4, call it 4.5. 4E remained in print, as well. This is truly a version 3, as the changes to character gen and combat are profoundly impactful on play.
5th Ed: Greg returned to design, made major changes to Character Gen (deleting the entire squire period), and his new math was, in essence, the same change to average outcomes as 4.5, which said, greg was VERY adamant it wasn't similar in outcome at all, that random in character gen was bad. (We exchanged about 6 long emails about it.) It's the fourth version of the rules.
5.1 was minor changes to 5.0, so version 4.1
5.2 was further minor changes to 5.1, so version 4.2 of the rules
6? I haven't checked.
A side branch, Paladin uses 5.2 as a baseline.
None of those editions are sufficiently different to be unable to use the characters of other editions, so adventures are usable... and hence ALL editions are "compatible"... but where it differs can dramatically alter the outcomes.
There is one element of 4.0 that isn't in any other edition: magic as a mechanic. And, per Greg, that was the worst edition addition ever; Me, I think it the best addition. YMMV... but, when 5th came out, 1st, 4th, and 4½ hit DTRPG.
Economics in editions: In KAP 1e, only bachelor knights are covered in Core; Nobles Book adds landholding.
KAP 3/4/4½ use a simplified single manor in core; The book Lordly Domains is a different mechanical approach from NB, and much more abstract, but also better at larger domains
KAP5.x has a single manor ruleset in core (pretty close to that of 4), plus Book of the Manor and Book of the Estate, for various more detailed and historic larger estates.
It should also be noted: 4½ was Green Knight Publications' edition. They were working on a lighter edition, but they only got the core and 3 adventure books out (The Tales of series). I don't know if they were going to do a magic book or not, but there was fan interest in a simpler one, especially one not using up to 10d20...