Regret is the emotion of wishing one had made a different decision in the past, because the consequences of the decision one did make were unfavorable.
John Greenleaf Whittier's fictional heroine Maud Muller gazes into the distance, regretting her inaction and thinking about what might have been.
Apologizing for a store closure, showing regret or remorse
Remorse is a distressing emotion experienced by an individual who regrets actions which they have done in the past that they deem to be shameful, hurtful, or wrong. Remorse is closely allied to guilt and self-directed resentment. When a person regrets an earlier action or failure to act, it may be because of remorse or in response to various other consequences, including being punished for the act or omission. People may express remorse through apologies, trying to repair the damage they've caused, or self-imposed punishments.
The Remorse of Orestes (1862), by William-Adolphe Bouguereau