tartan - usually reserved for kilts/skirts.
Tartan is a pattern consisting of criss-crossed horizontal and
vertical bands in multiple colours. Tartans originated in woven wool,
but now they are made in many other materials. Tartan is particularly
associated with Scotland. Scottish kilts almost always have tartan
patterns. Tartan is often called plaid in North America, but in
Scotland, a plaid is a tartan cloth slung over the shoulder as a kilt
accessory, or a plain ordinary blanket such as one would have on a
plaid - a synonym for tartan in the US
checkered - I think this is US-specific, not so much in the UK anyway.
check - contracted version of "checked" or "checkered", eg "check shirt".