Unless you have a specific example in mind, the two are different. A jest is a joke, and an object of derision is something which has been derided (fairly or unfairly).
To joke about something is not necessarily to deride it, especially since 'to jest' seems to be less intense than 'to joke'. We say 'it was only in jest', and we do not mean that we were only deriding someone or something.
Neither are the butts of the jokes necessarily objects of derision (with the exception of politicians). One can be the frequent target of jokes without feeling than one is being derided.
Student or Learner