My long-running 2e campaign could kinda be described as "magical cyberpunk set in the Age of Pericles Mediterranean (except it was really a Dying Earth/post-Singularity far-future)". Which is to say, I bet my 2e was nothing like your 2e. Were we playing the same game?
(I also think 3e gets unfairly reviled)
I guess I am not elaborating enough.
If you are using the 2e mechanics (AC, THAC0, Savings Throws, Levels, Combat System, Character progression system, etc) then the "content" is not relevant, its still the same game. For example, I know Ravenloft, Forgotten Realms, and the Outplanes are all 2e, even though the content is all different.
Let me try and clarify. 1E and 2E both use THACO, Levels, Armor Class, Classes and Races as a foundation. What really makes the identical is the Armor Class and THAC0 usage, and creatures are rewarded based on Hit Dice, not comparison against creature and character. Experience rewards were based on the creature, not the character to creature comparison. What set 2E asside was the inclusion of additional rulesets (most notably weapon specialisation and selection optional abilities) and the removal of some classes (which didnt matter too much as 2e made clear a path to add new classes all together).
3E has some of those similarities, but the change is more pronounced. Challenge Ratings, Feats, etc. change the core dynamics of the game. Not saying for "worse", just saying different.
I'm asking the logical question as what makes two games different. For example, because World of War Craft uses levels, races, and classes, does not mean World of War Craft is also Dungeons and Dragons.
Perhaps the copyrighted material is what ties all the editions together (such as Ravenloft, Greyhawk, FR, DL, etc..)?