I've been typing up my notes. But, I'm struggling to define vocal, falls, slides, and runs.

Could someone come up with simple definitions for these techniques?

Also, am I using the correct terms?

Nice work, Pip! Here are my definitions:

Fall: a (usually) short descending "fall" in pitch at the end of a note

Slide: a more gradual ascending slide from a lower pitch to a higher pitch

Run (or riff): more than one pitch sung on one syllable; usually 3 pitches or more in quick succession, with distinction between individual pitches without rearticulation