Muffin in non-North American English refers to a part-raised flatbread, like a crumpet. In North America, muffin typically refers to a sweetened quickbread baked in a mold like a large cupcake, but shockingly even less healthy. The rest of the English speaking world generally refers to this as an American muffin.
In North America, biscuit refers to a levened, typically unsweetened quickbread. For the rest of the English speaking world, a biscuit is flat, unlevened, and often sweet, like shortbread. This would be referred to in North America as a cookie.