An apology is an expression of regret or remorse for actions, while apologizing is the act of expressing regret or remorse. In informal situations, it may be called saying sorry.

Does apologizing mean you're wrong?

“Apologizing does not always mean you're wrong and the other person is right. It just means you value your relationship more than your ego.”

What is the true meaning of apology?

A real apology has three main components: (1) it acknowledges the actions taken and resulting pain inflicted on you; (2) it provides an action plan for how s/he will right the wrong; and (3) there is an actual change in behavior proving to you that there won't be a repeat of the past.