The question is: the difference between what in Hungarian?
But there are various levels of apologizing. It is different when you did something wrong and ask for forgiveness (you don't say "please excuse me for stealing your money") or when you simply inconvenience someone or unintentionally cause minor damage. I guess the less the damage, the less important which phrase you use. A simple polite form of asking for someone's attention is probably a minor offence. So, you can say "bocsánat", "elnézést", "ne haragudjon", etc.