you can use "affedersiniz" for two situations: 1: it can be said that in a question-answer context where the speaker and the hearer do not know each other, it functions as a kind of polite initiator of the communication. Example: Affedersiniz, bu çanta sizin mi? or: Affedersiniz beyefendi, saatiniz kaç? 2: when you did something wrong in a formal situation so you must say you are really sorry about this example: Sebebi benim eşekliğim, affedersin doktor bey. ------------------------------------------ ozur dilerim is an apology - it is I am sorry for an action and asking forgiveness - you are basically requesting a answer back

if you don't something wrong, you should not apologize. "özür dilerim" means; sorry. "affedersiniz" mean, excuse me. but there is not big difference in daily life.