Denote, connote and their corresponding nouns denotation, connotation are complementary rather than synonymous. Taken together, the verbs as used in reference to terms equal mean (see MEAN vb 2).
Taken singly, a term denotes or has as its denotation whatever is expressed in its definition: in a noun the thing or the definable class of things or ideas which it names, in a verb the act or state which is affirmed.
A term connotes or has as its connotation the ideas or emotions that are added to it and cling to it, often as a result of experience but sometimes as a result of something extraneous (as a poet's effective use of the term, or its constant association with another term or idea, or a connection between it and some historical event); thus, "home" denotes the place where one lives with one's family, but it connotes comforts, intimacy, and privacy.
What a term denotes (or the denotation of a term) can be definitely fixed; what a term connotes (or its connotation) often depends upon the experience or background of the person using it.
In logic denote and connote, though still complementary and still predicated of terms, carry very different implications.
They are dependent on two highly technical terms, both collective nouns, denotation and connotation.
A term denotes (or bears as denotation) the entire number of things or instances covered by it; thus, "plant" denotes the aggregate of all things that come under the definition of that word; the denotation of "plant" is far more inclusive than the denotation of "shrub."
A term connotes (or bears as connotation) the sum total of the qualities or characteristics that are implied by it and are necessarily or commonly associated with it; thus, "plant" connotes (or bears as connotation) life, growth and decay, lack of power of locomotion, and, commonly, roots and cellular structure invested with a cellulose wall.