A synonym is supposed to be any word that means the same as another word. But I don’t think there is any such thing. I don’t believe that kind of synonym exists.
Okay, I need to qualify that assertion. Technically, a synonym is “a word or phrase that has a meaning the same as, or very close to, that of another word or phrase.” So if your definition of a synonym includes words with similar meanings, then yes, I believe in synonyms.
But when you consider the meaning of a word, you need to consider both its denotation and its connotation. The denotation is the primary, literal meaning of a word. The connotation is the suggested or implied meaning of a word. Connotations usually come from experience or associations. Seeing a word used repeatedly in certain contexts gives the word a different color than it gets in the dictionary.
Connotations may even have accidental origins. Simply because one word looks like another word or shares the same syllable, even if technically the two words aren’t related, we tend to associate them together. For me, amazement carries some of the connotation of magic, partly because of its second syllable. And the sound of a word unconsciously influences its connotation. The word disgust would be a weaker word without the coughing, gagging g, the hissing, sneering s, and the spitting t.
Because I believe strongly in connotations, I don’t believe in synonyms. Because every word has a unique connotation, no word has exactly the same meaning as another. For example, the Random House Unabridged Dictionary uses as examples of synonyms the words joyful, elated, glad. But each of those three words has a different connotation! To me, joyful connotes Christmas (“Joy to the World”), a deep sense of happiness. The word glad carries a connotation of satisfaction. Elated, from the Latin word elatus or “raised,” has the more extreme connotation of excitement.
Each of those three words would be used in different situations or contexts. For example, when a friend admits that he got to the county park quicker when he followed your directions rather than his, you might simply say, “I’m glad that you agree with me.” But if you said, “I’m elated that you agree with me,” it would imply greater sarcasm. And you would never say, “I’m joyful that you agree with me,” because you wouldn’t feel a “deep sense of happiness” over something so unimportant. And do you know what? If you check the dictionary, joy, elated, and glad all have slightly different denotations too.
As I said, you can only learn the connotation of words by reading (a lot) and through experience. But your writing becomes incalculably more effective when you use the right word, instead of picking any word that seems to be a synonym.