According to my references, the terms "Longsword," "Broadsword," and "Bastard Sword" are appelations applied to later (Victorian era) scholars. In-period, a "longsword" (which was regularly used from horseback...IIRC at the Battle of Bourgtheroulde in the early 12th C one of the few cavalry charges conducted with swords occured) would probably have been referred to as a "sword." When sword design diversified enough -- with "longswords" developing a pronounced point to allow for an armor piercing thrust, but still retaining its slashing capabilities -- "longswords" came to be known as Arming Swords (i.e. the sword you wore at your side when in armor -- your side arm or backup weapon), while "Bastard Swords" were known as War Swords (the weapon you would use in war if that was your primary weapon, i.e. in lieu of a pollaxe or similar).
There were other bladed weapons that existed during the period of the ordinary sword (roughly from the fall of the Western Roman Empire to around the end of the 13th C IIRC), though these were different enough that they had their own names, or local enough that they weren't a major influence on the wider European culture.
As for the earlier slashing longsword of the 11th-13th C (the Classic D&D Longsword), this weapon did have a tip and could (and indeed was) used to thrust upon occasion. In an illustration from a German source (Jungfrauenspiegel, ca. 1200) shows a German knight who is clearly thrusting with his sword (it also shows, incidentially, another knight using an ordinary arming sword in a two-handed grip), while at the Battle of Benevento (1266), French knights found it difficult to defeat the German's coat-of-plates (Splint mail in D&D terms), so they began using their longswords in a thrusting method, directed at the armpits of the German knights, where the coat-of-plates did not protect. These swords were still of the old type and had a fuller down its length (later Arming Swords, which I like to call cut-n-thrust swords, had a diamond cross-section for strength).
One thing to keep in mind about Medieval European weapons nomenclature, during the period in question, such names seem to be haphazard and indistinct. A Voulge could mean a number of weapons, from a pure axe-like weapon with a pointed tip, to a weapon resembling a halberd or other pole-arms. Most of these names were applied during a later period.
Damon.