There is a certain relationship between these words, but they are not interchangeable.
"Certain thoughts may be associated with a word."
"A word can have different connotations depending on the context in which it occurs."
"Associated" denotes a relationship. "Connotations" is a property of something. It is a secondary meaning associated with a word.
"Words will often have different connotations associated with them, depending on who you ask."
Student or Learner