Not really. "chilly" is "cold and uncomfortable" while "cold" is just a fact.
"It gets chilly/cold when the sun goes down. Do you want me to get you a sweater?"
"The service was very bad and the food, when it finally arrived, was cold."
"That's what you need after a long days' work: a nice cold pint."
When I left for my trip to New York a few weeks ago, the last days of what we call "summer" here in the San Francisco Bay Area were coming to a close. It wasn't warm anymore, but rather cool, but I could still leave the house in a t-shirt, or maybe a light sweater. When I was in New York, oh my lord was it freezing! Me being from a rather temperate climate, I don't even own heavy winter clothing, so I had to bundle up in the heaviest lined and hooded coat I had (putting on two pairs of socks, some gloves and a lined hat which covered my ears); my nose and extremities hurt because it was so cold. I was glad to come home to San Francisco because, although it is getting colder (and getting darn near freezing at night), and the days are really getting chilly (no more, shorts, no more t-shirts, heavy sweaters for all!), it's still not as bitter cold as it was in New York.
There's a little narrative for you mestizo about how I perceive the use of the various adjectives in question.