Weapon skills can be acquired in one of two ways, either by pursuing an individual weapon type or the entire family of like-weapons at a greater cost. As an example your character might have a desire to train only in how to use his grandfather’s longsword, so acquiring skills in longswords specifically might make more sense.
Progressing skill in a single weapon takes less effort than an entire class of weaponry and therefore costs fewer skill points to advance. But attempt to utilize a weapon other than the one specified and you will be doing-so at a disadvantage.
A more brutish fellow might decide that they wish to be more utilitarian than that and be able to utilize any weapon within a specific family of weapons, such as any one-handed blade. If it’s got a blade on it and you only need one hand to wield it, they want to be able to pick it up and use it effectively. Whether you carry it with you or pick it up from the battlefield, if it is within the same family of weapons you can wield it without penalty.
Progressing skill in an entire family of weapons requires a great deal more effort and therefore costs more skill points to learn and advance.