Medical certificate contains all the basic information about your medical health, which is issued by a practicing doctor with his or her stamp and date of issuing that certificate.
Details like age, gender, weight,height, eyesight, any allergy or previous medical history is mentioned.
Your Character Certificate is issued by the institution for which you have pass perviously. It has the details for your behaviour and manners, that you followed in that particular institution.
Hope I made your doubts clear.
Thank you.