The main "types" of physics (maybe all natural science) are held to be theoretical, experimental, and computational, with some debate whether computational science is theory, experiment, or a 3rd category. I've recently seen data analysis added as a 4th.
My personal view is that computational physics is, if done "right", definitely a type of mathematical/theoretical research - but a lot of it is data churning; some sort of non-science. The same could be said of analysing big data and experimental science.