There’s no specific instance wide feud between the two or anything. At a high level, .world is just the biggest Lemmy server currently by MAU and .ml is just the oldest and flagship ones run by the main developers of the Lemmy software.

Now, the moderation philosophy between the two differs a fair bit, which is where the rivalries and the bad blood develops between users. On most general topics you’d see very little difference, but as soon as discussion touches the Russia-Ukraine conflict, anything negative about China, and the Israel-Palestine war, the mods on ml are aggressively one-sided in their moderation, and consider anything that goes against that perception as hate-speech against Russia/China/Palestine even if that’s not what you are saying. If you want an illustrative example, look in the modlog at the ‘nazi apologia’ comment I was tempbanned from !memes@lemmy.ml for.

Still, as community and instance managers, that’s their right. There’s significant overlap between lemmy.ml, lemmygrad.ml where moderation is more overtly this way, and hexbear.net where users like to communicate with image macros more in ways that I think most other server members find annoying. Some on world don’t like that so certain users crosspost discussions from ml communities onto world communities. Some users call the ml folks tankies for their disdain of violence committed everywhere except where committed by Russia, China and its allies. Some ml users (and many lemmygrad+hexbear users) call users on other servers libs for the converse reason, excusing or not pushing back hard enough on atrocities and oppression caused by Western governments. Some users like to generalize these characterizations to every user of an instance, it seems.

Aside from high profile defederations with ml or world and some servers for various reasons, refederations, redefederations between hexbear and other servers, there have not been any specific incidents that have caused .world and .ml to grow apart. I think it’s fine to let each server have its space.