No, but they come from the same general area of the cow - the flank or area between the ribs and hip.
The skirt steak is the diaphragm muscle. It is a long, flat piece of meat, with a tendency toward toughness. But it has good flavor. It can be grilled or pan fried quickly with good results. Another traditional method is to stuff it, roll it, and braise it. In many areas of the country (Texas, for example) skirt steak is the only cut to be used when making "real" fajitas.
The flank steak is the traditional cut used for London Broil. It is long, thin, and full of tough connective tissue. It is usually marinated before being broiled or grilled whole. Because it is tough, you usually slice it thinly on a diagonal across the grain to sever the tough fibers and make the flavorful steak chewable.