Not quite~

Each weapon has a Type.
Femur is staff, Flintlock is gun, Throwing knife is dagger, for example.

Each Type has three levels of competence. Every time you use a weapon to attack or activate a weapon skill, it will gain skill points in that type. Once you reach enough skill points a level will be gained in that Type.

To show an example: The pictured weapon is the Femur, which is considered a Staff-type weapon. Since your Staff skill is now level 2, it unlocks the skill "Bone Thwack" for the Femur.

If you took the Femur off and used a dagger type instead, you'd lose the skills that were for the Femur, but gain the skills you had for the dagger.

If, instead, you equipped a Wooden Staff you just picked up, it would have two skills - the original skill it came with and the skill it gets from having Staff level 2.

This way you can build up your weapon ability without having to worry that all your work on one weapon will disappear after it breaks. It will carry on over to any weapon of the same Type.

Also, while normal attacks will give one point each time, skills will give more points - so while they take more durability, they also add more skill points.