Plaids
We should really start by pointing out that, somehow or other, America has come to use the word plaid (pr: plad) as being interchangeable with tartan whereas, back here in Scotland, we reserve the word to describe the truncated upper portion of the great belted plaid, the feilidh-mhor or breacan-an-feile both Gaelic terms, the former meaning "large wrap" and the latter meaning "tartan wrap". Plaid comes from the Gaelic and roughly means blanket. Having dispensed with the semantics, now we can talk about them!
Long Plaid or Pipers' Plaid
This is a full length plaid which consists of
approximately three and a half yards of 54inch wide tartan (3.2 metres x
137cms) with the ends fringed. In Scotland this plaid is worn almost exclusively
by pipers in Pipe Bands, either civilian or Regimental. It is very rarely worn
by the individual as it is rather clumsy to wear.
A much larger plaid than the informal fly plaid and pleated as can be seen from both photos. 
Its origin in history was
that the long plaid was the upper part of the kilt or feile mor which was used
to cover the head and shoulders in bad weather. When not in use it was wrapped
around the body of gathered on either shoulder at the back to prevent impeding
the movements of the arms as much as possible.
Drummers will wear the fly plaid rather than the long plaid as they need
plenty of freedom for their arms and a long plaid would impede that.
Small Plaid or Fly Plaid
A Fly Plaid
There's no set size for fly plaids and they can vary from a small one about a metre (39 inches) square up to a larger one measuring about 1.4 metres (56 inches) square, to an even larger one of 1.8 x 1.37 metres (6 feet x 54 inches). Some have one corner gathered and sewn for pinning over the shoulder, others are ungathered so that it's easier to drape over the shoulders of a shivering partner and/or is easier to press (iron) if it gets crumpled.
It's important to order your fly plaid at the same time as your kilt so that both are cut from the same length of fabric - that way, they'll match exactly. Buying a plaid later on may result in a bit of a mismatch since the fabric may be from a different dye batch or even from a different weaver. Plaid & fringe photos below courtesy of Keltoi Celtic Clothing, Kitchener, Ontario.
Fly plaids can be plain fringed like this or . . . . 
. . . purl fringed like this.
