How does "denotation" differ from "connotation"?

In 2004, I asked Merriam-Webster the following question. Assistant Editor, Daniel Brandon, replied as follows.

Q: Denotation means “the totality of things to which a term is applicable especially in logic.” Connotation means “an essential property or group of properties of a thing named by a term in logic.”

So, whereas denotation refers to a word's dictionary definition, connotation means what the word means when people use it?

A: Your analysis is essentially correct, at least enough so for casual use.

The “denotation” of a word is its intrinsic meaning; the meaning that is attached to the word itself outside of any context or environment.

The “connotation” of a word is the meaning that is layered in when the context is taken into account; it presupposes a certain commonality of experience between the user and he interpreter of the word.

Thus, while the word “war” by itself may just denote a fight between large groups of people, its use by a European author in the late 1940s was undoubtedly influenced by images of World War Two, and readers of the same era would have immediately understood this.

On a lighter subject, one example I found was that while “rabbit” and “bunny” share the same denotative meaning, “bunny” has the connotations of a pet rather than a pest. A hunting license for “bunny season” would sound rather silly.