The Muffins "native" to the UK are like bread. English Muffins use yeast as the leavener.
In North America, an English-style Muffin is called an English Muffin. In the UK, an American-style Muffin is often called an American Muffin.
American Muffins are more like a cake. They are made from a very thick batter that is spooned into metal or paper cups, and when baked, look like a large cupcake.
The American Muffin can also be classed as a quick bread, as it uses chemical leaveners.
The more sugar and fat in an American Muffin, the more it is going to be cake-like. You usually mix all the dry ingredients separately, then all the wet separately, then combine. This not only prevents the chemical leavener from activating too soon, it keeps the liquid away from the flour as long as possible, because as soon as liquid hits the wheat, gluten will start to develop. You combine both just enough to blend: small lumps don't matter.
The two most common mistakes when making American Muffins are over-mixing, and over-baking. Over-mixing causes gluten to develop, which results in tough Muffins.
Always cool American Muffins on a cake rack. Let cool first, though, in pan for 5 or 10 minutes, then invert out onto the cake rack -- trying to get them out of the Muffin pan right away could cause them to fall apart, but leaving them in much longer than that will give them soggy bottoms that will just never recover.
"... Equally popular were the muffin men, who patrolled the middle-class suburbs around teatime, ringing their small bells (except on Sundays: they still patrolled then but went bell-less on the Sabbath.) [Nineteenth-century muffins were, of course, not American cake-like muffins. The modern 'English muffin' (an American anomaly, too) is the descendant of what was being sold here. Made from a yeast batter, they were cooked on a griddle rather than baked, then cut in half, and served hot, spread with butter.] They carried their goods in oilskin-covered baskets wrapped in flannel or green-baize lining to retain the heat, either over their arms or on their heads. Muffin men were young boys or old men -- that is, those who could not earn a better living in some other trade -- for the muffins generally came from one manufacturer, and his 'lads' had to pay for their own uniform of white sleeves and white apron, as well as the basket, blanket and bell. (Among the few sellers to carry goods on their heads, they wore caps rather than hats.) They received 3d for every 1s-worth of muffins they sold, and they could carry only a single shilling's-worth before the muffins got cold. Given those geographical and physical limitations, and the fact that most people bought muffins only at teatime, being a muffin man was not profitable." -- Flanders, Judith. The Victorian City. London: Atlantic Books. 2012. Page 285.
"In the 1830s, Dickens wrote that at teatime householders opened their doors and screamed out 'Muffins' with all their might." -- Flanders, Judith. The Victorian City. London: Atlantic Books. 2012. Page 288.
The fifth Sunday before Christmas , has in the Anglican Book of Common Prayer the following collect: Stir up we beseech thee, O Lord, the wills of thy faithful people... Consequently, it has become the day on which people stir up their Christmas puddings and Christmas cakes.