Here's some examples of what I mean:
Is there a general term for this? Is the term for the vocals version different to the term for the lead synth version?
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In terms of electronic music, the term "pitch bend" is probably the most common, easily understood, and appropriate term for both cases.
In a more classical/formal context, the musical term for this kind of continuous variation in pitch is portamento, which applies whether it is fast (as in your examples) or slow. This term applies to all musical instruments that allow continuous pitch variation, including voice. Sometimes the term glissando is used though this latter term usually indicated that you hit a set of closely-spaced discrete notes. The usual example of this is sweeping your hand along a piano keyboard. As an illustration of the difference between these general music terms in terms of synths, portamento is what you get if you mess with a pitch bend wheel, and glissando is what you get when you drag your finger across the keyboard.
Note that glissando and portamento usually involve going in only one direction (up or down). Your second, vocal, example returns to the original pitch, so these terms might not be the best to use (pitch bend should work fine though). The term melisma is particularly appropriate for this kind decoration in vocals.