Yep, those are hunter braids.
And I braid the button braids. Used to do hunter braids but I prefer the look of button braids. At the two-days I did in Area V we usually did dressage + sj, then xc the second day, one or two shows would occasionally switch it up. I prefer doing SJ first, especially if it's a one-day. It's like the warm up for cross country for me in a one day. XD