 For an 8 element braid, without a specific bead loading pattern on each cord, turning clockwise/right or counterclockwise/left won't make a difference. The reason it doesn't matter is because there are only two sets of elements to work with, and whichever direction you turn you will be working with the next set of elements you should be. For braids with more elements, be it 12, 16, or more, the direction you rotate changes which set of elements you are working with. This has both a visual and a physical structural effect.
If you look at the photo above, you can see that the left half of the braid is a smooth, even Z twist. On the right half, the braid is still a Z twist, but the "stitches" are uneven, and if you touched the braid, you would feel a ridge where the stitches are overlapping each other instead of lying next to each other.
This photo shows how visual elements are affected by the direction of disk rotation. The kumihimo pattern generators at Craft Design Online or Friendship-bracelets.net both build their pattern layouts on Z twist braids with counterclockwise/left turning. As you can see in the photo above, when you make the braid with a "modified" Z twist—that is, bottom left up, top right down, turn clockwise—the cords are moved out of order, leading to a broken or incorrect pattern in the braid.
Applications for the S and Z twist in expanding your braiding skills
One of the things I was most intrigued by when I started braiding was kongo gumi/round braids that changed directions as they were made. Once you learn the S and Z twist, you can combine them to make some beautiful pieces.
This is a 16 element S and Z twist braid made with four colors that shows the directional changes make the braid into chevrons.
This 16 element braid was done with eight elements of each color to make wide chevrons.
This eight element beaded braid not only alternates S and Z twist, it has beads.
The secret to changing between S and Z twist is this: Flip the cords in each pair. In these illustrations, I am showing only one set of cords, but you would do the same with each pair of cords in each set of elements you are working with.
Before the flip, showing the cords to flip. You should flip right over left when going from S to Z and left over right when going from Z to S.
After the flip of the cords at position 32. Make your flips WITHOUT rotating the disk.
I hope this post has explained the difference between the two directions of kongo gumi/round braids and that you will try them both out, and experiment with changing directions in your work.