Crêpes are a kind of pancake, which are very thin. While German and Scandinavian pancakes are thicker, American breakfast pancakes are typically even thicker.
In American pancakes baking powder or other leavener is often used to raise the batter. Another trick is to whip the egg whites separately before carefully mixing with the yolks to achieve even fluffier American pancakes. However, the French crêpe as it is served on the street or in a restaurant, is thin so it can be easily folded, wrapped, or rolled. Sometimes sugar is added to the batter. In contrast, a kind of savoury crêpe made out of buckwheat is the galette, of northern French origin. Both the wheat crêpe and the buckwheat galette are intended to be used with fillings, from the most basic: a sprinkle of powdered sugar, to jam, chocolate, or even nutella. Crêpe Suzette is a sweet version made using liquor and then enjoyed with a spectacular flambé. Wheat crêpes can also be served in savory combinations: with cheese, herbs and creme fraiche (French sour creme), or mushroom stew.
Regarding recipe and technique, some crêpe recipes call for substituting half of the milk with water in order to achieve an even thinner batter. When making crêpes at home it is essential to use as little batter in the pan as possible. This can be achieved by either tilting the frying pan in a circular motion or by pouring off excess batter. A thinner batter will spread faster through the pan and will take longer to solidify, so thin crêpes are easier to make using a batter that is thinner than for regular "pancakes". Finally, there is no baking powder in an authentic crêpes batter.
Essentially, crêpes are a kind of thin pancakes.