Twisting is to hold the brush tightly and turn it, which is a big action.
Twisting the tube is to gently hold the brush and let it rotate between your fingers. This is a very small action.
I guess you are also a calligraphy lover. I think it is very important to write Chinese brush and writing brush. If you want to know the basic knowledge of brushes, you can find this article and read Top Ten Brush Brands in China (with brush selection and maintenance methods).