This is my take, with no attempt to back it up:
Language refers to things (real or not). This is true of any comprehensible bit of language, whether a single word or a phrase. And it is true of both spoken and written language.
The relations between a given bit of language and what it refers to (referents) are sometimes divided into these categories:
Denotation: the set of direct, or general referents. This is sometimes called the (basic) meaning of the words.
Connotation: meanings that expand on the denotations, by including feelings, associations with given contexts, and the like.
The distinction is relative. Depending on the scope of attention, the boundary between the two can shift.
Examples of denotation and connotation for the word house:
The word house denotes (among other things) a particular kind of building or construction, not so much in terms of appearance as in terms of function.
The word house, in its use with that denotation, typically has connotations that involve feelings of shelter, family, etc.
The word house can denote a governmental (typically legislative) body, such as the US House of Representatives or the UK House of Commons.
The word house, in it use with that denotation, can have connotations that involve feelings of cooperation, deliberation, stuffiness, bureaucracy, formality, etc.
These are single-word examples. Like house, the multiple-word House of Representatives is also a name, so it is easy to see that the same descriptions apply. Similarly, any noun phrase.
But even a non-noun phrase or a sentence, such as She liked me on Facebook or You can't win them all, can have associated feelings and contextually specific connotations.
The connotations of a given bit of language refer to all of its possible meanings. And "meaning" is taken widely here: it refers to all possible subjective effects. That includes effects in the minds and feelings of listeners and readers, and it includes effects in the mind and feelings of the speaker or writer.
Connotation is about larger, subjective meaning. The thing that is referenced in connotation is not just the thing denoted (physical, real, or not). It is that denoted thing plus all of the subjective and psychological effects that referring to it (i.e., using the given bit of language) entails.
Connotation is about the thing as not just something separate from the people referring to it (thing in itself). It is about the thing as being, or as including as part of itself, a set of social relations and psychological states or effects.
(Just one opinion.)