there is no mathematical difference, only a visual difference. In algebra you tend to use a vinculum as it looks neater and is easier for writing long division rather than using brackets.
A vinculum is a grouping symbol; for instance, if you want to write "the square root of 6 + x", you can write the square root symbol followed by "6 + x" in parentheses or you can attach a vinculum to the square root sign and write the "6+x" with a bar over it (the vinculum) instead of using parentheses.