You are correct, 'Play Sins' gives you just the base game content, or 'vanilla', as it's commonly referred to here on the forums.  'Play Entrenchment' gives you starbases and other content.  'Diplomacy' gets you everything.  This also comes in handy when you want to play multiplayer with someone that doesn't have all of the expansions.

There was a lot of confusion over the difference between Diplomacy and Trinity when the games first came out, too, so don't worry, you're not alone.

Hi. I got the boxed version of Trinity today. Set up this account and tried to register my CD-Key but it said it was invalid. I tried reentering it in different ways about 20times but not joy.

How did you get it to work? 

General rule for Stardock serial numbers is to only use numbers (0-9) and the letters A-F, and make sure to include the dashes.

IIRC, Trinity/Diplomacy 1.00 corresponds with Entrenchment 1.05 and Sins 1.19

The only patch since then was a technical fix that addressed a multiplayer crash issue.

Yes, though they're still quite formidable.

As far as I can tell, 7DS is not currently compatible with either Entrenchment or Diplomacy (or even just the original game when fully-patched).  If you're not willing to dual-install, you're probably better off waiting for Danman to create a compatible version (which it seems he's working on).