I always thought of the difference as Dennotation is from the dictionary and Connotation is how we connect to the word.
My favorite example is the difference between:
He claimed he was 18.
He stated he was 18.
He admitted he was 18.
In a dictionary the definitions aren't that different but our reaction to them is. I won't let my students right that a patient "claimed" to be in pain since the connotation is that the pain is not real.