Scones (UK usage) are a quick bread, usually moderately sweet. They are baked on a sheet pan, sometimes sliced into wedges,sometimes cut into rounds or other shapes. They are similar to, but sweeter than American style biscuits.
Biscuits (UK usage) or cookies (US usage) are very small, flat cake-like confections, usually rich in butter and sugar. They are also baked on sheet pans, in individual portions typically only a couple of inches across (although sizes vary widely). They come in a myriad varieties and flavors.
Typical flavorings are vanilla, chocolate, nuts, citrus. Some of the simpler varieties allow the butter flavor to come through.
Biscuit (US usage) or tea biscuit (UK usage, one variant) are a type of quick bread charactarized by flat, flaky layers. They are typically cut in rounds a couple of inches across, and tend to be about an inch tall. They are usually only very lightly sweetened if sweetened at all.
Tea biscuit (UK usage, another variant) or teacake are biscuits or cookies traditionally served with tea. They tend to be fairly neutral in flavor.
Muffins (UK usage) or English muffins (US usage) are small yeast-raised breads which are griddled in rings, rather than baked in an oven. They tend to be a couple of inches across, and about half an inch tall. They are often split and served toasted.
Muffins (US usage) or American Muffins (UK usage) are a quick bread, usually moderately sweet, baked in single serving portions in muffin tins (the same pans used for cupcakes).