Most websites and cookbooks agree that crumpets and English muffins are different, although they all disagree exactly how.
Crumpets and English muffins are both griddle cakes - meaning they were originally made on the stove top in a cast-iron griddle pan. They are both round and generally biscuit-sized. They both have a spongy texture full of nooks and crannies for absorbing melted butter and other toppings. They are also both considered to be a breakfast, brunch, or tea food, but not the kind of bread you would serve with dinner.
Crumpets are always made with milk, but English muffins are not.
Crumpet batter is a loose batter. English muffins are usually made from a more firm dough.
Crumpets are made only using baking soda. English muffins are usually made with yeast or sourdough.
Crumpets are cooked only on one side, so the bottom is flat and toasted while the top is speckled with holes. English muffins are more bread-like and toasted on both sides.
Crumpets are served whole with jam and butter spread on top. English muffins are usually split before coating and serving.
A regional variation of the crumpet is the pikelet, whose name comes from the Welsh bara piglydd or "pitchy [dark or sticky] bread", later shortened simply to piglydd. This spread initially to the West Midlands, where it became anglicized as "pikelet", and subsequently to Cheshire, Lancashire, Yorkshire, and other areas of the north. The main distinguishing feature of the Welsh or West Midlands pikelet is that it was traditionally cooked without a ring, with an end result rather flatter or thinner than a crumpet.