The term "tartan" refers to a pattern of threads woven together. There are many different tartans, and Scottish clans traditionally hold claim to one particular tartan.
The term "plaid" refers to a length of cloth, of a tartan pattern, wrapped and draped about the Scotsman, as shown below.
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So, tartan is a pattern, and plaid is a garment.
And that lovely tartan ribbon (above)...well, look for that to show up trimming a Christmas stocking for the shop later this year. But until then, have a Happy National Tartan Day!