Is the filter used in the film age called white balance in the digital age?

Not exactly. It should be said that the color temperature in the film age is called white balance in the digital age.

There are many kinds of filters, one of which is color temperature compensation, and then there are UV filters (to prevent the negative film from being too blue, but they are generally used as protective lenses) and polarization filters (to eliminate polarized diffuse reflection). Filters for black-and-white photography have a special purpose, which can reduce the contrast of other colors except one color. For example, a yellow mirror can shoot a dark sky and the clouds look very white.