'Atonal' vs. 'Freetonal'

'Atonal' has been loosely used to characterize any music that is what I would call 'non-modal' (tonality being, I would argue, a form of modular modality in which the prevailing/governing scale type is completely saturated with cadential fictae).

Some music merely ignores the conventions of modality/tonality, while other music deliberately eschews many of the defining devices and effects of modal/tonal music. This second type of music, especially including serialism, is the central reference point for all things 'atonal'.

It's not a very quick process, but I'm gradually persuading music theorists that serial atonality has more in common with tonality than it does with a lot of other non-modal music. To hear it in the way Arnold Schönberg implied we should hear it, we really have to hear the serial row and the sonroities that result from its various co-impositions as the partial de-verticalization of all possible non-tonics; the perpetual disideration of the resolute is an extension of the idea of the key-defining dominant chord. In this way, I hear (or at least have reason to try to hear) serialism as a sort of minimalization of Wagner's device in which dominant follows dominant, and in which that to which these dominants are heard as to be pointing is seldom, if ever, actually heard. In both cases(Wagner and Schönberg), the assumption is that we hear the dominant (and other putative non-tonics) as necessarily pointing to a tonic. This was probably almost entirely true of people in Wagner's world and Schönberg's world, but is less true today, and a lot of people (Americans especially, I think) don't quite 'get it', due to our greater exposure to overtly modal and nonwestern musics, and things like Debussy and Stravinsky. The blues, in particular, is characterized specifically by one dominant being followed by precisely the wrong next-dominant according to European tonal grammar, and the scale content is usually the opposite of anything we might hear as 'corrective' ('corrective' might include Mahler's leading tones added to dominant chords).

Depending upon in which language you study, you may be exposed to terms that more accurately translate as 'free-tonal' rather than 'atonal'. This is a more loose idea, even to the extent that it could include instances of the effects of tonality. Berg's work is quite like this. Tonality and 'atonality' co-mingle to whatever extent he seems to think will best facilitate his chosen narrative at any particular point.
I don't think of Ligeti as being 'atonal', but a lot of his work could probably be fairly described as 'free-tonal'; strong scale implications tend to result from most of his pitch choices, so it's fair to assume that he's using scales... he just doesn't let them use him.