Let me preface this questions with letting you know that I have just started to look in to our family genealogy.

Would someone please explain how the two part of Clan MacLeod fit together (based on tartans and clan cap badges)?

I have been looking at the history of MacLeods and how they can be traced to Leod, who was born about 1200, the son of Olaf the Black, King of Man and the Isles. Leod married the daughter and heiress of MacRaild about the year 1220. Through his son, Tormod, came the MacLeods of Harris, Dunvegan and Glenelg, and through his second son, Torquil, came the MacLeods of Lewis.
According to the Clan MacLeod Society website the badge of MacLeod of MacLeod bears the motto 'HOLD FAST', while that of MacLeod of Lewis is 'I BURN WHILE I SEE.' The badges do not show a separation of clanship, but rather a togetherness, and a shared loyalty to one another.

However (stay with me here is the question), now it appears that the MacLeods of Lewis (Loud MacLeod tartan) is also called MacLeod dress on many websites that sell kilts. So is it possible the someone wearing a MacLeod of Lewis kilt (as MacLeod dress) would wear the MacLeod of Harris cap badge but usually wear the MacLeod of Harris tartan while not in a formal setting? When and how would you match the tartan to the cap badge?
I hope that long winded question/rambling didn't confuse too many people.
Any ideas?