Half-board borders are often used in place of standard 1-2 board borders, especially when the main purpose is to cleanly cover the ends of cut deck boards, without the need for bringing the fascia up to cover the deck board ends.
It is also a time-saving alternative to a standard border, which usually requires the addition of extra framing and blocking along the outer edge of the deck to support all boards involved (this is generally not necessary with a board-rip border, provided that the rip is narrow enough.)
In addition to fastening the rip to the framing, partial-board rips can be fastened through the outside of the board rip and into the ends of the cut boards, to keep the seam between the rip/decking tight, clean, and flush.
Rips can be as wide or as narrow as the installer desires, depending on the application or desired effect. They can also be cut so that the textured surface is facing up (see above image) or so the rip is facing out (see image below).