No one knows exactly what the knife that James Bowie carried with him at fight that happened at the dueling grounds outside of Natchez in 1827, popularly known as the Sandbar Knife Fight. This knife was given to him by his brother Rezin who later remembered it as having a blade of about 10". This is the fight and the knife that got the bowie knife craze started and it had long since been lost by the time of the Battle of the Alamo. The "bowie" knives that were carried after this time were largely English made blades of an English design. It is doubtful that the original blade was a pure fighting knife because it also seemed to have been use to butcher large game, though he did carry it as a sidearm also. He did this because he had once been shot by a local sheriff whom he was having an argument with even though he had shown the sheriff that he was unarmed. It might seem to be strange that he should sellect a knife instead of a pistol but you need to remember that a pistol back then was largely a single shot affair with a not entirely reliable ignition system. Keep in mind also that once you pulled the trigger on one, whether it went bang or not, all you had left was a second rate cudgel.
As far as what a fighting knife is, it's largely what at hand when things get up close and ugly. Most didn't carry a specialized fighting knife, they just used what they had on them.
Doug