Overlay, superpose, superimpose, appliqué can all mean to add one thing to another by placing the former upon or over the latter.
Overlay usually implies covering with another material or substance, sometimes thinly (as with a wash, glaze, or coat) or sometimes thickly (as by encrusting, veneering, or plastering).
In extended use overlay usually implies accretions or additions that conceal or encumber the original thing or smother and stifle whatever there is of life in it.
Superpose and superimpose are not always clearly distinguished, especially when they imply a putting of one thing on top of another, thereby extending the height of the original mass; thus, strata are layers of rock successively built up by sedimentary deposits, each layer being superimposed or superposed on the one previously formed.
Superpose, however, is more often chosen when relative position only is indicated, and superimpose when the thing added rests upon or is supported by the original thing; thus, superposed columns do not necessarily have the columns of the lower row for their respective bases, but superimposed columns do; an overtone is strictly a superposed tone.
Superpose is also the technical term when dealing with light rays or other energy waves that occupy the same position without destroying each other or losing their identities.
Superimpose often, especially in extended use, carries the implications of imposition or the addition of something extraneous and unintegrated.
Appliqué basically implies an ornamenting with pieces, usually of contrasting material, that are cut or shaped and applied (as by sewing or pasting); the term is used primarily in reference to textile ornamentation.
In extended use appliqué suggests overlaying with something obviously added and forming a pattern.