In chapter 12 of How to Read Like a Professor, there's a line about symbolism that says: "Even in a fairly clear-cut case, we can't pin down a single meaning, although they're pretty close."
I like this line for two reasons. One, it's an indirect reminder that synonyms are not interchangeable, and that writers should, when necessary, always shoot for the exact words.
And two: multiple meanings mean multiple layers of interpretation mean lots and lots of discussion and debate! And being a puzzle guy, I like figuring those things out.