Formally, if $f$ is a function, $f(x)$ is a value. So for instance, $f$ can be continuous, but not $f(x)$. In teaching at school and university, notation is quite often mixed up, e.g. the function is called $f(x)$. This may be problematic but can also have benefits. What good reasons for the use of the different notations do you know?
This question raised from the discussion of this discussion on notation of derivatives.