JustEnoughItems functions as both a server-side and a client-side mod. Because it only requires the data that’s already on the player’s computer to run, it will work perfectly well even if the server the player is connecting to doesn’t have it installed.

Does OptiFine need to be on server?

OptiFine is a client-side only mod, meaning it only needs to be installed on your computer in order to run. Installing it on a server, for which it was not designed for, is going to cause performance problems, if not outright crashing.

Based off of NEI, JEI modifies the existing Inventory GUI by adding an icon list of items to the far right. This list is useful for checking recipes and uses for items, and can also be used to search for items in opened GUIs. JEI has a lot of addons, generally adding extra modded recipe support like Thaumic JEI.

Is JEI a client?

Can JEI run client-only, or with a vanilla server? Yes, with some features disabled: The “Move items into crafting area” [+] buttons.

JEI doesn’t have cheat buttons, those are from NEI. To put JEI into cheat mode CTRL+ click the wrench next to the search bar.