I don’t know if they are right or if I’m also misinterpreting this. From what I know sponge basically be able to do what forge client and server side mods were able to do. But instead its all server side and players won’t have to download and install any mods themselves. Is this correct?
This is more or less correct, some details missing but as far as understanding for the end user goes this will suffice.
Clients will only need to install mods if Sponge is released for 1.7.x, as Forge doesn’t allow connections from non-forge clients yet, although we’ve been told they will by 1.8. That aside, Sponge will be a server side API, much like Bukkit/Spigot, and more similar to Cauldron, although the server isn’t built into Sponge. Sponge is a forge mod, so it sits on top of the Forge server. Because of that, it might be able to add extra support in their API for mods, although I don’t know if that’s confirmed or possible for sure.
It sounds like someone told you that Sponge will enable mod-like content on a vanilla client from the server alone, and it definitely won’t be able to do that. If it enables this sort of functionality at all, it’d likely require a Forge client with Sponge installed, then, if the idea of a plugin repo is sorted out, it’s possible the server can prompt the client to download ‘safe’ plugins, if they need client-side support. But as it stands, Sponge is primarily a server side only thing, and will likely function in a very similar fashion to Bukkit short of it being on a Forge server.
If you want to see what is so far what exactly sponge will be and won’t be able to do, I would check these links if you haven’t yet.
Additionally this gives a bit of an overview on what sponge can run on top of.
I’m not exactly sure if this is what you are looking for, but I hope this helps you a bit.