From what I can tell, some sennit is laid and some is braided. Usually we see the laid type but here is an NZETC article on Samoan technique showing the braided type and 3 illustrations:
http://nzetc.victoria.ac.nz/tm/scholarly/tei-BucSamo-t1-body1-d4-d4-d7.html
Figure 1 shows the regular sequence
This figure shows one "add-on" sequence
Final figure is another "add-on" sequence
From what I'm gleaning in a quick read this braiding type is good for everyday purposes but is not as good as laid sennit.