What's the difference between unappreciated and unvalued?

Unappreciated

Definition:

Example Sentences:

Definition:

(a.) Not valued; not appraised; hence, not considered; disregarded; valueless; as, an unvalued estate.
(a.) Having inestimable value; invaluable.

Example Sentences:

(1) The fact that so many are now turning their their backs on a career in the NHS is an appalling reflection on how unvalued the profession feels.” There are fears that next year’s figures could be even worse as a result of the bitter dispute between junior doctors in England and Jeremy Hunt, the health secretary.
(2) This is an unvaluable advantage, especially if this contributes to maintain or restore an often precarious health.
(3) It’s as if the presence of the building is valued and gives this area of the city an identity, while its actual fabric remains unvalued, not worthy of the investment to rectify and revive it.
(4) Whatever is unexamined with marks and tables is unvalued under the Gove whip.
(5) There is a deep contradiction in the attitudes of a society which celebrates equality in principle yet treats some people, especially the poor and vulnerable, as unwanted, unvalued and unnoticed,” the bishops write.
(6) Many doctors in training feel alienated, unvalued and deeply frustrated and this extends far beyond the current contractual dispute.