At this point, wouldn't it be a demo?
That depends on the functionality. In a demo you can usually follow the story up to a certain percentage to just get a feeling for the game if you would like it or not. In a beta you usually play for finding bugs and glitches and balancing problems. Therefore almost the complete game is available or at least the parts the beta testers should test.
Demo = there should be no bugs (polished)
Beta = just the current state of the game (event. unpolished)
@meme
I think the release date on 2nd July is realistic or Larian would already have announced a delay. You can patch a digital (and even physical) release until the final day of release (famous day-one patch). I'm more concerned about the almost non-existing marketing for Dragon Commander atm. Since the end of the kickstarter campaign for D:OS I haven't heard a single piece of news about DC anywhere on the web. That's not a good sign for a game which is to be released in about a month.....