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I got the stuff about "septs" from a website (by googling williamson and clan).  It just means a division or offshoot, I think.  The trouble is that "Williamson" is an extremely common patronymic which would have arisen all over the UK independently, so proving one's descent from those who were part of Scottish clans would be difficult.  If you've got back far enough to establish a link, good for you.

Ref williamson clan which in  gealeac  was mac William son of william aglisized williamson
the clan was scattered as the clan chief tried to size the the throne of Scotland in either 900 or 1100 AD
hence no clan members of the clan. we were protected by clan gun or clan mackay hence the septs
also the williamson in Ireland were sent to ulster during the plantation so the irish williamson are of scots decent the English williamson so we're from the saxon and Norman name wilhelm  and the sons became son of wilhelm  williamson I am an ulster williamson you can tell if the are of scots descent if the are Presbyterian and if they are Catholic  they inter married in the south of Ireland they are of english/Norman mainly around Dublin