Is this an incorrect use of the word 'Synonymous'?

"Robespierre is synonymous with the Great Terror in the French Revolution".

As far as I know, when things/words are synonymous with one another it's because they have a similar meaning.

However, I've heard statements similar to the above many, many times. Is this an alternative and correct way of using 'synonymous'. If so, under what grammaticality is it correct?

Not only do the various dictionaries have entries like this:

synonymous adj
2. Equivalent in connotation: "a widespread impression that . . . Hollywood was synonymous with immorality" (Doris Kearns Goodwin).

But you can see that renowned writers like the one cited above (she wrote, among other things, A Team of Rivals: The Political Genius of Abraham Lincoln, on which the recent film about Lincoln was based) use it in this figurative way all the time.

I don't know why people want to shackle language with the fetters of abject denotation. Figures of speech are what make language interesting, rich, and broad. A pox on pedantry, I say!

The use is fine. Check out definition 2 here http://www.merriam-webster.com/dictionary/synonymous

: having the same connotations, implications, or reference