Synonyms are frequently said to be the vocabulary's colours, tints and hues (so the term shade is not so inadequate, after all, for those who can understand a metaphor). Attempts at ascribing to synonyms the quality of interchangeability are equal to stating that subtle tints in a painting can be exchanged without destroying the picture's effect.
All this does not mean that no synonyms are interchangeable. One can find whole groups of words with half-erased connotations which can readily be substituted one for another. The same girl can be described as pretty, good-looking, handsome or beautiful. Yet, even these words are far from being totally interchangeable. Each of them creates its own picture of human beauty. Here is an extract in which a young girl addresses an old woman:
"I wouldn't say you'd been exactly pretty as a girl — handsome is what I'd say. You've got such strong features."
(From The Stone Angel by M. Lawrence)
So, handsome is not pretty and pretty is not necessarily handsome. Perhaps they are not even synonyms? But they are. Both, the criterion of common denotation ("good-looking, of pleasing appearance") and even the dubious criterion of inter-changeability seem to indicate that.
In conclusion, let us stress that even if there are some synonyms which are interchangeable, it is quite certain that there are also others which are not. A criterion, if it is a criterion at all, should be applicable to all synonyms and not just to some of them. Otherwise it is not acceptable as a valid criterion.
Types of Synonyms
The only existing classification system for synonyms was established by Academician V. V. Vinogradov,