There are a myriad ways to hold a knife. There are a lot of ways to cut/slice/dice/core/flay/peel/stab/etc a person. A really good knife fighter will be able to transition or change the blade in mid movement while retaining control of the knife. There is *no* correct way to hold a knife. There are pros and cons of each and it is best to know them *all* well.

You want to learn them? Find a good arnis/kali/escrima/silat school. Find a good knife fighter. Find a quality school that teaches how to use a knife. But, quit thinking inside the box about "correct" or "proper" ways to hold a knife. That can get you killed.

IMO,
Mark