There’s some nuance here, but ultimately both terms have a seat at the table in this discussion. I definitely have lyrics with elisions, especially mid word when there are multiple consecutive vowels.
The omitting of syllables also happens frequently in the poetry of hymns, so elision is correct be it mid word or between notes.
It appears, based on these definitions, that some elisions may also be liaisons. Regardless, this glyph can be used in both ways.