lettering vs piece of writing

lettering and piece of writing both are nouns.

Word	Noun	Adjective	Verb	Adverb
lettering	Yes	No	No	No
piece of writing	Yes	No	No	No

As nouns, piece of writing is a hypernym of lettering; that is, piece of writing is a word with a broader meaning than lettering:

lettering: letters inscribed (especially words engraved or carved) on something
piece of writing: the work of a writer; anything expressed in letters of the alphabet (especially when considered from the point of view of style and effect)

Other hypernyms of lettering include writing, written material.

lettering (noun)	piece of writing (noun)
letters inscribed (especially words engraved or carved) on something	the work of a writer; anything expressed in letters of the alphabet (especially when considered from the point of view of style and effect)