What is the difference between the words "dormant" and "latent"?

Here is a brief explanation of the difference between latent and dormant in James Fernald, English Synonyms and Antonyms (1914):

That which is latent (from L. lateo, lie hidden) is hidden from ordinary observation (compare HIDE); as, latent powers; a latent motive; a disease is said to be latent between the time of its contraction and its manifestation. Dormant (from L. dormio, sleep) applies to the winter condition of hibernating animals, when they seem to sleep, or are even apparently lifeless; we speak of dormant energies (which have acted, and may yet again be aroused); a dormant volcano volcano; ...

Webster's Dictionary of Synonyms (1942) places latent and dormant in a larger group of related words that also includes quiescent, potential,and abeyant:

Latent, dormant, quiescent, potential, abeyant (or in abeyance) agree in meaning not now manifesting its existence. Latent implies concealment and is applied to that which is present without showing itself; dormant usually suggests sleeping and is applied to that which is alive without manifesting activity; as, a latent talent; latent energy; a dormant plant or volcano. "The poet's gift of seeing the latent possibilities in everything he touched" ([John Livingston] Lowes). "Which power can never exercised by the people themselves, but must be be placed in the hands of agents, or lie dormant" (Ch[ief] Just[ice John] Marshall).

Fernald's example of a latent disease is apt because, even though the germs may be proliferating madly inside the infected person's body, there are no symptoms yet—and as a result, the presence of the disease is hidden. A dormant disease, in contrast, is one that a person has had in the past but that has ceased (at least temporarily) to be active—and yet may be reactivated under the right circumstances (as when the body's built-up immunity to it breaks down).