Checks come in a number of different styles, though the best known among them is probably the plaid. Plaid in American English is synonymous with tartan, the check patterns most closely associated with Scottish clans.
In British English, particularly in Scotland, plaid refers to a thick tartan cloth used both as a blanket and thrown over the shoulder when wearing a kilt.
What plaid is not synonymous with is check, which describes any fabric with crossing vertical and horizontal stripes.
With the exception of a legitimate Scottish tartan worn as part of a formal occasion, checks are always less formal than solids or stripes.