I too find it confusing but I think it's like this:
Minecraft/specific game curseforge is this site here we are typing on (or at least I am) which is for the game your after the content for.
Curseforge is the interconnected between all games and their community content, I assume Twitch Launcher uses this one, also alphas aren't shown for Twitch which the same applies here unlike minecraft.curseforge.com [just tried with 2 mods (Transmatrics a dead 1.10 tech mod and Mappy an alpha very alive 1.14 Fabric mod) I know are in alpha/experimental but are accessible on minecraft.curseforge.com and both didn't show up on curseforge.com/the interconnected/Twitch Launcher content download using site]. (curseforge.com)
and Curse is their own company website rather than their game community content services websites. (curse.com)
Niche Mod Finder/Acknowledger/Tester/Player. Fan of Datapacks, Rift 1.13/1.13.2 Mods, Fabric 1.14 Mods and interesting underrated or new 1.12.2 and below versions of mods. :) Testing 1.13.2 Forge and Fabric 1.14 mods mostly though.
I sometimes create the odd modpack or adventure map once an idea comes together.