Are ladyfingers and Genoise made the same way?
Delicious variations abound, so it is hard to make absolute statements of what is "officially" a ladyfinger.  In my pastry class, we were taught that the classic recipe for ladyfingers is close, but not identical, to genoise.  Store-bought ladyfingers can be anything from, essentially, a meringue to a shortbread cookie.

Foam-based batters -- i.e., those that do not use chemical leveners or yeast -- can be divided into two categories: whole-egg and separated-egg.  The main difference in results is that the latter tend to be stiffer and can better tolerate being overcooked a little.  The primary example of whole-egg batter is the genoise cake.  Because the whites are whipped together with the yolks (and sometimes extra yolks are added), it is a finicky batter, requiring more skill to assemble properly than others, but when it works, it is more tender.  Separated-egg batters are far more common, as they are easier to assemble; the key is that you whip the whites into medium-to-stiff peaks, then fold it back into the rest of the batter.  Examples include chiffon, dacquoise, and the French "biscuit" cakes.

Most recipes for ladyfingers use a separated-egg batter; others use a simple meringue.  The meringue version will make a crisp cookie, the version with with the yolk, soft.  Either will work well for uses like tiramisu or trifle.

Here is a recipe for ladyfingers from Allrecipes.com and a recipe for genoise from Epicurious.  For my ladyfingers, I add a pinch of salt and some flavorings, such as vanilla or nut extract, but the base recipe is essentially the same.