Non-harmonic and non-chord tones are the same thing. They don't belong to a common chord. 

There is a skip and a step (seconds or thirds +)

passing tone

escape tone

neighboring tone

appoggiatura

accented passing tone

accented neighboring tone

anticipation

suspension

retardation

changing tones

double neighboring tones/group

non harmonic tones make the transitions between chord progressions sound better and smoother. it fills the silence between each half note chord as well.