Melodies are a succession of notes moving through time, one at a time. Melody is the proper term for what some some call the “tune”.
Melodic shape and melodic rhythm are two factors every melody uses in some way. Melodic shape is the general direction the melody moves in terms of pitch: up, down, sideways. Melodic rhythm is the rhythm(s) applied to the pitches.
Many other elements fall within these two categories. Some are: tessitura, interval spacing (the distance between two notes), the use of arpeggios, chord tones, scales, non-chord tones, syncopation, and many others.