Beyond Divinity continues some of the story from Divine Divinity, though DD2 (in development) should be more of a 'second part'. Not much info has been released on DD2, but I would expect it to be more of a direct continuation of the DD story.
In Beyond Divinity there are 2 main characters, and summoning dolls that you can use as characters (with some limitations) or just as mules to carry extra loot. Except for that, the controls are fairly similar to DD. You can give both characters commands at the same time, or select them individually (the non-lead character can be set to aggressive, to attack automatically).
BD is divided into 4 separate acts, so is not quit as open (or occasionally overwhelming) as DD, but there is more variety in environments. The skill system and alchemy were changed, and another couple stats were added (which makes deciding where to assigning stat points more difficult, but allows much greater flexibility in character creation).
There is a
demo (168MB) available you can try, which includes the first level of the first act in the game. As with DD, the beginning was designed to be relatively linear. After the demo was released there were a few additions made, like party selection and screen re-centring hotkeys, and the voices were re-recorded (opinions differed on which were 'better').
If you are expecting BD to be just like DD you may be disappointed, but generally if you liked DD you'll probably like BD as well.
There are various opinions and comparisons (and possibly spoilers) in the topics;
Convince meThinking About Getting Beyond Divinity 
