Tartan is the cloth where the plaid is made of. Not the “blanket” itself.British English speakers would just say blanket but it may be a regionalism. Plaid is a kind of fabric or the tartan sash in traditional Scottish Highland costume. US English speakers say plaid to describe the pattern or type of weave but GB English speakers call it tartan.
A plaid is the “ blanket” used for picnics and when travelling by train, or on a chilly night in front of the fire.