Underpin vs Underlay - What's the difference?

In transitive terms the difference between underpin and underlay

is that underpin is to support from below with props or masonry while underlay is to put a tap on (a shoe).

a layer (of earth, etc.) that lies under another; substratum.

(underpinn)

To support from below with props or masonry.

You should underpin the mine roof to prevent further collapse.

(figuratively) To give support to; to corroborate.

Public confidence in politicians must underpin our democracy.

(head)

(underlie)

To lay (something) underneath something else; to put under.

To provide a support for something; to raise or support by something laid under.

to underlay a cut, plate, or the like, for printing

To put a tap on (a shoe).

To incline from the vertical; to hade.

(en noun)

A layer (of earth, etc.) that lies under another; substratum.

A soft floor covering that lies under a carpet.

Anything that is underlaid

(music) Lyrics; or more specifically, the way in which lyrics are assigned to musical notes.

The underlay in bar 3 is unclear in Handel's manuscript.