As far as I know Sage Bracket and Space-Time bracket are same .. Is it true ? ( I just want to confirm what I know, if someone pls tell me about it )

What I want to know is that -

Let's assume I'm from S678. Suppose my space time have players from S600 - S700. So a player from S537 or S 724 can't participate in my space time right ? They have their own space time. My space time has only players who is from Server S600 to S700.

And here is my question - so is my sage world has same people from S600 - S700 only, right ? A player from S712 or S544 can't join my sage world, is it true? There could be multiple sage world battlefield between players from S600 to S700, but a player from other server than this will never join these sage world right ?