MacDonald of the Isles

[Nathan]

There are tartans called MacDonald of the Isles but from my research I can't find any clan/branch called MacDonald of the Isles.

Does anyone know if this is simply a tartan specific term? Is it a synonym for another branch (i.e. Sleat/Clan Donald North) or does it apply to all MacDonalds from the Western Isles regardless of Clan?

I know there are several branches both with chief and without including

Clan Donald (aka Macdonald of Macdonald = all of the branches)
Clanranald
Glengarry
Sleat (AKA Clan Donald North)
Keppoch (AKA Clanranald of Lochaber)
Antrim
MacAlister

And ones with no chief:

Dunnyveg (Aka MacDonald of Islay and Kintyre)
Glencoe
Ardnamurchan

And cadet branches of other branches like:

Boisdale
Glenaladale
Kingsburgh (?)

I'm also confused about the status of:

MacDonald of Lochalsh

There are tartans that are confusing because I'm not sure they correspond directly to clan branches, though perhaps they do, such as:

MacDonald of the Isles (the subject of this query)
MacDonald Lord of the Isles (I'm thinking this applies to all MacDonalds)
MacDonald of Staffa

Are some of these just titles bestowed on idividuals and not Clan branches per se?