Plaid and tartan are both crisscross patterns of two or more colors, but the key difference is that tartans have a recognized name or history. Tartans should always be woven from wool, with each locality having its own favorite designs.
Plaid garments for kilts and other Highland dress date back to the 16th century in Scotland. In the US, tartan refers to plaid associated with a clan, while plaid means any checked cloth of two or more colors.