If two words are synonymous, they mean the same thing. You tried to convince her that "love" and "chocolate" were not synonymous, but it was no use.
In addition to describing words with the same or similar meanings, you can use the adjective synonymous to describe things that are similar in a more figurative way. Summer is synonymous with picnics, playing outside, and days at the beach. Summer is also synonymous with ants, skinned knees, and sunburn!