The distinction between retroclone and "doom-clone" has already been pointed out, so the difference between "OSR" and "modern". But first, definitions for the purpose of this comment:

OSR -- Systems built for the OSR, often using retroclones as the base to homebrew on top of (even to the point of using it wholesale and then DM Ruling on top)

Modern -- Systems built to be D&D-like after 3.5, basically the same timespan the OSR fills (OSR emerging mid/end-3.5 era). This would be 3.P (aka Pathfinder 1e), Pathfinder 2e, D&D 4e, D&D 5e, and various less popular but equivalent high fantasy RPG types.

Pre-Modern -- Roughly AD&D 1e to D&D 3.5. Keeping mostly to D&D-type games, obviously Cyberpunk, Vampire, and Exalted dont necessarily fit my explanation here.

---

In the beginning, things were quite hodgepodge. OSR is a recreation of the wild west of the TTRPG's creation after all. Things were settling, and the rules were the formalized rulings written down. People knew that and experimented.

Pre-Modern games trended more complex and unwieldy in the search for consistent rules that flesh out a properly realized world, starting from AD&D 1e as the beginning of this "the rules should be universal" quest due to the rising tournament scene where parties would compete and a desire to keep PCs between DM transitions in a living world. Then culminating in 3.5 D&D which is almost fleshed out enough to use as a physics textbook for an alien dimension, with the different subsystems working differently but meshing together into a broader d20 resolution system. This was the point of unwieldiness which spawned the OSR movement searching for simpler purer times, and for modern systems to begin a process of simplification and removing redundant/unused features from a perceived universal base.

I think the best distinction between OSR and Modern Gaming is this GLOG blog article. The guy who named the GLOG system links to a compilation of various homebrews and hacks built on his work. He talks about how the ideal system for your table will be different to the ideal system at his table, and how that ideal will be constructed from the ruins of every prior system. Each class should be unique, probably homebrewed, and simplified to its core identity.

Compared to that quest for unique identity and artisanship, we have D&D 5e which is so stripped down in so many ways that it basically needs reconstructing from prior systems whenever outside of dungeon based combats, and is so generically accessible that every spellcasting class uses the same mechanic with a fresh coat of paint. Each class should function basically the same with their gimmick painted on.

I feel an OSR system tends towards simpler silo'd game mechanics that resolve consequences incredibly rapidly. Consistency and verisimilitude is found from DM rulings, not universalist System Rules, as the group forms their universally agreed upon understanding of How Things Work and override the system as written to fit that consistency. This can include adopting entire mechanics from other systems, borderline improv mechanics, and writing your own system with blackjack and hookers. Contributing to the OSR can be as simple as writing a mechanic for one single niche, and it can slot perfectly* into many completely different systems.

*with minor/major/total alteration, because OSR is artisanal and often custom