Quick answer: Liquid Notes is a songwriting assistant software that analyzes single- and multi-track MIDI arrangements and enables deep modification of those, whereas Garage Band only supports one track.
How Liquid Notes differs from Garage BandGarage Band can essentially be seen as the little sibling of Apple’s flagship DAW Logic Pro, providing a rather reduced feature set though. Most points mentioned in the article describing the Differences between Liquid Notes and a DAW apply to a degree. Find this article here - http://re-compose.desk.com/customer/portal/articles/1401894.
Unlike Liquid Notes, Garage Band does not provide a musical analysis of chords or chord progressions, or any other harmonically constituting properties.
Garage Band communicates with Liquid Notes via the Mac’s internal IAC bus - but on one MIDI channel only and is therefore useful only in the context of a single-track arrangement. Liquid notes creates an exact read-out of existing chords - providing standard chord symbols and a piano-roll view. The built-in technology of Liquid Notes provides the user with all the tools necessary to further control, change and extend any chord, or any succession of chords, without having to re-record (or input) the music again.