It should be noted, before I start wandering here, that all the various kinds of swords we have put names to were just called "sword" in their day. Most of the names are from archaeologists attempting to sort out the timeframes of grave goods.
Oakeshott typology is probably the most famous way to sort what GURPS will call a "broadsword" and D&D will call a "longsword."
GURPS has a list of swords that are all "broadswords" under the rules.
Khopesh
Broadsword
Large Falchion
Pata
Shotel
Bastard Sword (used one handed)
Dao
Estoc
Hook-Sword
Jian
Katana
Longsword
Backsword
Cavalry Saber
Edged Rapier
The D&D 5e equivalent to "broadsword" is "longsword" and it covers a wide variety of side-arms. Perhaps more because the "versatile" tag means it can be used 2-handed; which would imply bastard sword is included.
This is a continuation from 4e where the weapons list is a bit longer, but still much shorter than 2e. I don't have any 3e books (or 3.5e books for that matter).
2e was longer than AD&D.
D&D, starting with 4e makes a distinction between "simple" and "military" weapons. 5e calls the distinctions "simple" and "martial."
With how over-the-top inclusive Wizards of the Coast went, I cannot but wonder if these categories are from the thinking about "assault weapons" among liberals.
The historical divide over some weapons is related to sumptuary laws in that you needed to be of a certain social rank to have them.
Cost wasn't the only reason a peasant didn't have a sword in many places.
But ahistorically egalitarian D&D can't make the common/noble distinction and still have adventurers, so...
I'm amused to note that 2e has a firearm, an arquebus. It also adds the rapier. 4e and 5e don't have guns, but keep a sword that was developed from guns driving armor off the battlefield.
Warhammer FRP is even more consolidated, most everything is a "hand weapon"
Hand Weapon: This broad class includes one-handed axes, swords, clubs, maces and hammers. These weapons are all comparable in use and effect, and no distinction is made between them in the rules.
Yet it still has a rapier...
Pathfinder 2e follows the same pattern as D&D (shocking! I know) but breaks the falchion out from longsword and still has a separate bastard sword.
Rapier without firearms again...
LBB Traveller has guns, so many guns...
Sword is the one handed, all inclusive sword. Broadsword is a two-hander. Cutlass is loosely defined enough to include a rapier.
Top Secret might have rules for swords, it definitely has rules for throwing them...
Top Secret SI has a "sword".