Gonna try to keep this as brief as possible, and this is based on a recent discussion
Tonality has two generally accepted definitions in the music world, both of which are mentioned in this great thread about modes.
One deals with functional harmony, a hierarchy of chords related to their context where groups of notes push towards resolution tendencies (cadences), most notably (but not exclusively) V-I or V-i. This is the stricter definition of tonality.
The opposite of this definition would be, generally speaking, modality. Atonality is a contrasting term, but is not antonymous with this definition of tonal harmony.
A looser definition would deal with the concept of key centers, a pitch (and possibly chord) where the music is most settled/at home. This includes both functional harmony as well as modality as described in the linked thread above.
The opposite of this definition would be atonality, the lack of key center.
Atonality is not to be confused with cacophony, poor writing, or chromaticism, although to some people atonal music may be cacophonous or poorly written, poorly written music and cacophony may sometimes be atonal, and chromatic writing may sometimes be atonal in limited contexts.
I didn't find the right solution from the Internet.