Sandbox and MetaVerse are mostly the same, just some minor differences (e.g. relations can't be set higher than friendly in MV) and your set of xml-files that bring the variables for the game with are checked if within their limits. That is, you can play anything in a sandbox game, mod or whatever, but in a MV game you'll be flagged if you submit such a game.
The campaigns are a strict set of sandbox-games, the intital ones will limit you in the techtree, or give you an accelerated start. Please note that each version (DL, DA and TA) has it's own campaign, but in the UE you can start them intertwined, and this can shatter the whole concept. For example in DL you can have a tactic to storm to the DL planet which wil be rent apart in DA by the speed-nerf, and TA has a harsh economy... Thus there is real difference between the versions.
In TA the MV-equivalent of the campaings are the 4 tournaments - they are controlled games of a fixed setup, mapwise.