In theory, yes. Even in practice, I can only think of one case in which they applied those rules differently (but it was a doozy).
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If you’re referring to Henry VIII, then you’re labouring under a misapprehension. Henry was not seeking a divorce; he was seeking an annullment, which was at that time part of Roman Catholic canon law, and continues to be so to this day.
The grounds on which he sought the annullment was that he had married his dead brother’s wife: Katherine of Aragon had previously been married to Henry’s older brother, Arthur, who died young. Not wanting to lose the Spanish alliance that the marriage had sealed, Henry VII had young Prince Henry marry the widowed Katherine.
By some interpretations of some biblical passages, that marriage was a breach of canon law. If so, then Henry’s marriage to Katherine was void from the start, and could be so declared by the Catholic church under its canon law relating to annullment.
Unfortunately for Henry, the Pope at the time was in a precarious position: the Holy Roman Emperor had occupied Rome with his armies. Since the Holy Roman Emperor was Katherine’s nephew, he put considerable pressure on the Pope not to grant the annullment. That decision by the Pope contributed to Henry’s decision to split the Church of England from the Roman Catholic Church.
Henry subsequently obtained the annullment from the Church of England. However, the canon law used by the Church of England was essentially the same as the canon law of the Roman Catholic Church relating to annullments. It was not a divorce.