Short answer: nope.
Long answer: both are swords, of course. The "long sword" and the "broad sword" both refer to the same kind of sword: the sword with two edges, a non-functional point at the end of the blade, a cruciform guard and a hilt designed for one hand. The main differences would account to what the long sword actually stands for.
During the Dark Ages, most swords still had the size of what we consider now as short swords: barely a foot in diameter. Most of the swords were based on the Roman gladius and spatha (gladiusand spatha, IIRC, both mean "sword" but the former is on Classical Latin while the latter is on Vulgate) It wasn't until the Celtics began to experiment with enlarging the blades before the swords began to differ from the Dark Ages swords; Celtics found that by adding slight chunks of metal into an already forged blade, they could pretty much extend the size to the size they wanted. Celtics also made hilts that were designed with ease of grasp in mind, but that barely survived into later designs. Of course a Celtic "long-sword" wasn't actually as long as later "long swords".
Hand-and-a-half (from which "bastard" swords derive) were swords designed for ease of use in one hand, but that could be used with two hands if necessary. A hand-and-a-half is slightly longer, slightly wider, and heavier than a typical "long sword", so you need a strong arm to use it; however, when you have the need (such as when you had to thrust, since by that moment the blade points were made fit for thrusting), you could use the hilt and also a bit of the blade. You see, before hand-and-a-half swords were made, warriors used the blade as a second hilt to thrust their weapons; this was dangerous since you could cut yourself with the blade. Thus, the hand-and-a-half swords extended the blade a bit, made the edge around a hand's length higher from the guard and left said area edge-less, and extended the hilt half a hand's length to aid in that thrusting. Hence, why they're called "hand-and-a-half": because the hilt was, in a way, extended to half a hand's length, and because they could be used both one-handed and two-handed.
Of course, what I'm telling you isn't entirely trustable (I'm recalling this from memory). In this case, Wikipedia could be a bit more useful than me, but I'd really recommend you looking for history books about the evolution of weapons, which should be available in a local library. I hope this helps, but I'm not as enlightened as you may think in that area (however, I DO am a sword enthusiast, and like to read a bit about it)
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