Neither Bracelet or Bangle since it's solid but with a clasp. Personally I call them  Banglets but I don't think that will catch on.

It's a clever and and attractive design since once you clip the clasp on it's basically invisible and doesn't interfere with the lines of the Banglet as a whole.

In this case the band is about the same width as the Cross, so this is an uncluttered effective and powerful symbolic piece.