noun
words of regret; expression of remorse
Used when someone expresses regret or remorse over something, often in a personal context.
彼は自分の失敗について悔やみ事を口にした。
He spoke words of regret about his own mistake.
noun
words of condolence; message of condolence
Used when expressing sympathy or condolences, especially in the context of a death or misfortune.
I offered words of condolence to the bereaved family at the funeral.
悔やみ is a more general term for condolence or regret, while 悔やみ事 specifically refers to the words or messages expressing those feelings.
Compound of 悔やみ (くやみ, 'regret, condolence') + 事 (こと, 'thing, matter'). The exact historical derivation is uncertain.