Two games from the same company with similar names? No, there is no connection.
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Actually, Beyond Divinity is set 20 years after Divine Divinity, and continues some parts of the story. It occurs in the same universe, but in a different realm. In BD you visit a couple places from DD and see various references to Rivellon, but do not need to have played the first game to play the second.
BD was based on the same game engine as DD, so the look is similar, though there are a variety of different environments in BD. Characters and NPCs in BD are in 3D, so are more configurable than in DD, and there are more types and varieties of equipment. The background in both games is in 2D.
