anyway, if you hold a sorry, it means you feel sorry, so 抱歉 means exactly I am sorry. that's all.
if you want to say a sorry, you must supplement to whom you say the sorry or for which reason you say the sorry. so if u use 道歉, you must use it like this: 为...something....(而)道歉 or 向...somebody...道歉 为 means "for" 为.....something...道歉 means say sorry for something 向 means "to" 向...somebody...道歉 means say sorry to somebody
now u understand huh~~~ good luck