I'm putting together a 1.20.1 Fabric Vanilla+ modpack (with Create), and offloaded many mods into datapacks to try to keep the number of mods in the pack down. I stumbled across these 3 software and people refer to them at the same time basically interchangeably. I was unable to find a comparison, and then I noticed I was familiar with 2 mod authors, Yung for Paxi, and Darkhax for Open Loader, both having mods in my pack.

What's the difference, and why would I want to use one vs another?

From looking at descriptions and other metadata, I can tell that Global Packs has been around for a long time, so that means that Paxi and Open Loader probably solve something it's unable to do so. Paxi and Open Loader only have a few Github issues, which is good, but they are newer, so that makes it moot.

Reddit post from 2 years ago says https://old.reddit.com/r/feedthebeast/comments/xvrtst/question_is_there_any_difference_between_paxiopen/ all three are like toothpaste, which doesn't explain anything.

While I'm here, can you point me in the right direction of how to properly distribute the datapacks into the modpack so that they stay on their respective platforms? I was actually looking to solve this problem when I was redirected into these 3 mods, which was another problem on the todo list anyways. I'd like to eventually post the modpack for strangers to use, and you're not supposed to just redistribute a massive zip file with the game files and mods all together. I'll be building the pack with PolyMC, which has a built in downloader for Modrinth and Curseforge mods. It's also related to MultiMC and Prism. The pack is primarily Modrinth, but there are a few on Curseforge.

cross linked YUNG-GANG/Paxi#40 Darkhax-Minecraft/Open-Loader#43

OpenLoader exists because Darkhax didn't know that Global Packs existed.
Paxi exists because back then, Global Loader was Forge Only.
They are all interchangeable, and mostly differ in the config format, pick whichever you prefer.

Regarding your mods, you will not be able to upload the modpack,
if mods come from two different platforms. You got to pick one, or the other.
(Curseforge has a list of mods allowed from other platforms, but I doubt all your mods would be in that list)

And regarding datapacks, Modrinth installs them to into the Datapacks folder, if you keep them in there, it should export properly.
Curseforge installs them into the resourcepacks folder (this will change soon), keeping them in there will also handle everything automatically.

P.s. if you have further questions, feel free to join our discord https://discord.brazier-modding.net
Or ping me on one of the many modded discord, my handle is jtk222