I haven't been able to come up with an exact quote proving the vows were the same or not but I strongly think they're the very same. The reason the vows were created was because the night's watch is a neutral order. Designed to defend the realm of Men, and in order to do so in the best possible way, they had to be independent to the houses and ruling parties in the 7 kingdoms, when someone takes the black he is supposed to start anew, even in a family point of view (See Maester Aemon's story for example).
The story you're mentionning however is kind of different. The 13th lord commander of the nightwatch has broken the rules, as his marriage was considered as "UNHOLY". Not only that, but he was also corrupted by the wicked powers of the wife he took. He started a war against the seven kingdoms. And that story was used along the books to explain why the wall is well protected from the north and not at all from the south. Because the lords of the seven kingdoms learned their lessons from that war. This lord commander was defeated and his memory was deleted from history.
The sorceress he took for wife/queen is believed to be one of the Others. And this story also marks one of the few times, the king beyond the wall joined forces with southern kings. Only hinting at the gravity of the situation back then, similar to the actual events.
It is still a legend though, I have read throughout the books (forgot where exactly TBH) that Bran heard nanny tell this tale and say he was a Bolton. However, we don't know if that is true or not.
A much more detailed explanation is here
This story was expanded in the 3rd book of ASOIAF: A Storm Of Swords. When Bran, Hodor, Jojen and Meera arrived at the nightfort. Bran was scared because he remembered old nan's stories of what occured there. One of the stories was the night king story:
"He had been the thirteenth man to lead the Night's Watch, she said; a warrior who knew no fear, "and that was the fault in him" she would add, "for all men must know fear". A woman was his downfall; a woman glimpsed from atop the Wall, with skin as white as the moon and eyes like blue stars. Fearing nothing, he chased her and caught her and loved her, though her skin was cold as ice, and when he gave his seed to her, he gave his soul as well.
He brought her back to NightFort and proclaimed her a queen and himself her king, and with strange sorceries he bound his Sworn Brothers to his will. For thirteen years they had ruled, Night's King and his corpse queen, till finally the Stark of Winterfell and Joramun of the wildlings had joined to free the Watch from bondage. After his fall, when it was found he had been sacrificing to the Others, all records of Night's King had been destroyed, his very name forbidden."Some say he was a Bolton", Old Nan would always end. "Some say a Magnar out of Skagos, some say Umber Flint, or Norrey. Some would have you think he was a Woodfoot, from them who ruled the Bear Island before the Ironmen came. He never was, he was a Stark, the brother of the man who brought him down."
-A Storm Of Swords, Chapter 56, Bran.
What can be noticed here, is the wall was composed of "Brothers", so no women were around just like in the present time. Except for the Night King's wife of course, hinting to the fact he was breaking the rule and reinforcing the idea that "Unholy" was a description of the vow breaking by the 13th lord commander of the Night's Watch. Hence my answer.
