A good part of this page is speculation. I just thought I'd warn you first. If anyone has any evidence to contribute, please send it along.
Where do the names come from? One way to learn about names is to look at maps of where the names are present today. Generally (not exclusively), Pitards appear in France, whereas Pittards appear in England. Searching for the names on a site like ancestry.com also illustrates this, as well as the fact that the American immigrant ancestors for Pitards and Pittards seem to have arrived from France and England, respectively.
However, Pitard and Pittard would seem to be variants with a common origin. How so? The surname Pitard seems to be most common in the the north and west of France. This region of France was for many years in the middle ages contested territory, fought over by France and England. One might theorize from this that different branches diverged when "Pittards" migrated to England with the Normans. This doesn't mean that the family split in the year 1066—Normans went back and forth for centuries after that—but it does hypothesize an origin to the relationship.
There are early French Pitards who can be identified. (To digress briefly, I must admit I'm VERY wary of any family histories which stretch back beyond about 1600. Some do appear on this website which come from well-documented sources, but I make no promises. The modern, skeptical notion of history which I'm very fond of was an unknown concept during and before the Renaissance, when the point of history was often to create what we would call a myth. You can even see this idea in more recent family histories—people seem to like basking in the reflected glory of their ancestors, even in "classless" America. Genealogy should instead be a way to connect to history, and this requires some historical accuracy. One can, of course, trace families back that far, but you can't rely on contemporary histories without some heavy lifting to document them.)
With that caveat, the Pitard family on this site seems to trace its origins, via New Orleans and the Caribbean, back to the towns of Chanteloup and Corps-Nuds in Ille-et-Vilaine, and before this to the towns of Teillé and Mouzeil in Loire-Atlantique. All of these fall within the area traditionally called Brittany (Bretagne). One of the earliest traceable Pitard ancestors, happily named Bon Pitard, seems to have been the man to move from Teillé to Corps-Nuds.
There are other Pitards. There was a Jean Pitard in the thirteenth-fourteenth century who was famous for being the first surgeon of St. Louis and the founder of the College of Surgery. I have seen no research on his family, however.
As a curiosity, there are two coats of arms associated with the name. I do not know anything about those who was awarded the arms, or why; consequently, I have no idea of how they might be connected to later Pitards. The families may have died out. In any event, these are descriptions of the two coats of arms, taken from Dictionnaire de La Noblesse, Par De la Chenaye-Desbois et Badier (Paris, 1869): Vol. 15, cols. 904-05 (which gives no more information than this):
PITARD, en Normandie, Election d'Artagentan; Famille qui porte pour armes: d'argent, au chevron de geules, accompagné en chef de 2 roses de même, & en pointe d'une hure de sanglier de sable, défendue & allumée du champ. (These are the arms in the image to the right). PITARD, autre Famille de la même Province, Election de Domfront, dont les armes sont: d'azur, au faucon d'argent, empiétant une perdrix d'or.
On this side of the Atlantic, there have been different groups of Pitards who emigrated from France to North America: there are references on the 'net to Pitards in Canada, though I have not found any relation between Canadian families and the Caribbean and New Orleans family that Pitard.net documents.
The Pittards are a Southern family whose history seems especially concentrated in Georgia. One family history site that cites sources on the subject is The Sarretts of Georgia. Also, I have seen references to a book entitled Pittard Family History by Anne Clark Bowden. Aside from these coincidental hits while surfing, though, I know nothing about them. I have encountered Pittards who seem to have appeared Louisiana and lost a "t" in the process. For what I know of this, see the "Notes" to the New Orleans immigrant ancestor, Louis François Pitard.
Oh—and the name has nothing to do with being hoisted. A "petard" is a small bomb used to blow open a wall or a door. To be "hoisted with one's own petard," as Hamlet implies (that's where the saying comes from), happens when the "engineer" destroys himself with the metaphorical backfire from his own plots:
For 'tis the sport to have the engineerSeveral crafts do meet in genealogical research, but I fervently hope that it will not be the means of my own destruction.
Hoist with his own petard: an't shall go hard
But I will delve one yard below their mines,
And blow them at the moon. O, 'tis most sweet,
When in one line two crafts directly meet. (3.4.205-210).