Cadential idea
This is a term introduced by Caplin1 (well, probably in an earlier work2) that is not thoroughly defined. It effectively refers to the content of the cadential function. This content is typically formulaic in nature3 – you will see very similar cadential ideas across different pieces from different composers.4 They often include a falling contour.3
For a cadential idea to be... well, cadential, it needs to have a cadential progression. It will also end with a cadence.