How can I tell by looking at the mod page?
How do I know if this will be server-wide if I install for my server, or if it's just for my client?
I read it again and again and I don't understand what you want exactly ? If you can develop you question and give more details
SHAREit MX Player
Something like buildcraft that adds items into the game isn't just a client-side mod, everyone on a server that uses it would have to install the mod, but I'm asking if there's any official way to tell for any mod
unless the mod page states otherwise just assume the mod is required on both the server and the client