There are reasons I prefer weapon equivalency over weapon groups: some weapon groups are true, others are not.
Using real life terminology for a while, there are many two-handers, just as a long sword is a much different weapon from a single-hander or arming sword, and you definitely cannot compare a(ny sort of) gladius to a rapier - which, in fact, where very long swords, unlike the weapons we commonly have in mind, the epée, and foil, also known as smallswords - or a cut-and-thrust sword…
On the other hand, other weapons are truly a little different; I generally don’t expect someone who can use a poleaxe to be unable to use a halberd, unless he tries to use it as a spear or to trip an opponent - which you cannot normally do with a poleaxe and, should you ever try that, would not have proper knowledge of.
Weapon equivalencies work thus: each weapon belongs to one or more groups; whenever a weapon may be used in the same or a similar manner as another weapon in the same group, that weapon can be used thus as if you were using that other weapon, but with all benefits applied to this weapon.
For example, a person who is proficient in a polearm that allows you to trip another can use any similar polearm to trip (and, presumably, attack, if the are similar enough - bladed and slashing, for example) another with no penalty on the attack roll.
Another example is the use of the Black Strike technique; one should be capable to employ it with any of these base items: a sword, dagger or knife in the main hand, and a dagger, knife, buckler, club, gauntlet or cloak in the off hand. All similar weapons can be thus used.
Note that the above weapons are mentioned in the Havens sourcebook and, generally, are historically accurate. Actually, the weapons of choice would be a rapier or cut-and-thrust sword in the main hand, and a dagger, main-gauche, buckler, or gauntlet in the off-hand.