Brush Script’s name describes it well: it’s a script typeface that looks as though it was drawn quickly with a brush. Its flowing forms suggest speed and fluidity. It adds a lively informality to headlines.
The lowercase letters are drawn so that they usually join, as they would if they were written by hand; they give the impression of being written by a signpainter. And this typeface has been used for exactly that sort of purpose for decades. It was originally designed as a metal typeface by Robert E. Smith for American Type Founders (ATF) in 1942, when making a script typeface that seemed to join seamlessly was a daunting technical undertaking.
Brush Script has only one weight, and by its nature it has no italic style; nor does it have a more upright style. The capital letters are meant to go with the lowercase; they are not meant to be used together in all-capitals setting.