Emotional effects are what you feel. Cognitive effects are what you know.
What do you mean by "this" stressor?
Cognitive effects would involve analysis of facts.
Emotional effects would deal more with your evaluation of these facts. If they are evaluated as "good," they can lead to your feeling comfortable, happy, joyful, elated or some other positive feeling. In contrast, if they are evaluated as "bad," you are likely to feel uncomfortable, sad, depressed, angry, fearful or some other negative feeling.
Your success in dealing with a stressor (whatever it is) will effect both your emotions and your assessment of your abilities.
I hope this helps a little more. Thanks for asking.