Is it correct to understand that talaq (divorce) does not take effect when its phrases are used for explanation or conversation, and not with the intention of initiating divorce, given that the speaker's own intention is the reference for determining intent?

Divorce does not occur merely by the utterance of the word without intention, such as when narrating a story, teaching, a slip of the tongue, a mistake, or addressing someone named "Taliq" (divorced) by her name. However, if a man addresses his wife with the word of divorce intentionally, even if in jest, the divorce occurs, based on the Prophet's (peace be upon him) saying: "There are three matters whose seriousness is serious and whose jesting is serious: marriage, divorce, and return (to marriage after a revocable divorce)." As for non-explicit phrases like "Go to your family," divorce does not occur unless it was intended by them. The husband is not allowed to claim jesting if he uttered an explicit divorce pronouncement intentionally.