Sorry

Sorry means...

You did not mean what you did.

You won't do it again.
You aren't seeking to gain anything out of the word and take full responsibility and consequences.

You respect what the other person wants because you hurt them. It won't be the same.

Actions over words.

EXAMPLE:
You left someone out of an invite to your party.. you say 'sorry'.. they don't invite you to their party, but you didn't say 'sorry' just to go to their party so you understand their decision, if you are truly sorry.