"Signal" has always bugged me because it has the connotation of a function of time, whereas historically the Fourier series were first used to represent functions of space.
It doesn't need to be time- and frequency- based. For example in quantum mechanics you transform from position to momentum space. I think the complaint was that the word "signal" excludes this later case while "function" is more general.
And notice that time is a component in each of these.