Clan association may be via direct blood lines or by way of chosen association. "Septs" are families whose names differ but who opted to join the "clan".
To complicate the situation some clans are clans in their own right while being members of other clans. An example is our family name Gair. It is a distinct clan with its own tartan MacGair or Gayre. It is a recognised sept of the Ross clan. In case you are not totally confused so far, it is a recognised alias for the clan MacGregor!