Many collectors are confused by these terms. They hear them from time to time. They may have some vague idea of what they mean. Let's clear up the confusion.
An essay is a proposed design for a stamp. The design was not adopted though. The design differs in some way from the issued stamp. Some essays are for stamps that were never issued. Some essays may closely resemble the final approved design of a stamp. Essays were used to evaluate the different possibilities for a stamp design.
Proofs come in two forms, die proofs and plate proofs. Both are for issued stamps. A die proof is an imprint of the die block itself. A plate proof is an imprint of the full printing plate. Sometimes you'll hear the terms "small die proof" or "large die proof". That has nothing to do with the die itself. It relates to the size of the paper that the proof was printed on. These proofs are in the same color as the issued stamps, or in a color very close to the issued color. Printers prepared these for the USPOD to examine and approve them before going to the printing press.
Trial Color Proofs are also in the same design as the issued stamp, but they come in varying colors. Most trial color proofs are die proofs, but a few are plate proofs. These were produced in different colors from the issued stamp to determine which color looked best before going to press.
I only scratched the surface on essays and proofs here. There is so much more to learn. If you want to learn more about these issues, the bible to read is "Easays For US Adhesive Postage Stamps" by Clarence W. Brazer. Most philatelic literature dealers will have copies available.
I donít carry essay or proof material. My esteemed colleague, James E. Lee, is an authority on essay and proof material. You can find Jim online at www.jameslee.com. Or by regular mail at: P.O. Box 36, Cary IL 60013-0036. Tell Jim I sent you.