Does "on your opponent's 3rd turn" mean after 3 turns?
The function of the card hasn't changed, but the wording change isn't great.
The new wording creates ambiguity in what &quot;third turn&quot; means, but only one interpretation makes logical sense for gameplay, even if it's the less likely meaning under the rules of English. It looks like they wanted to be more specific on when it's destroyed (the end of your opponent's turn rather than the start of yours) which was a bit unclear in the original wording. There's definitely a better middle ground between the two card wordings, one that specifies 3 turns from when it was played perhaps something like this:

After this card's activation, it remains on the battlefield for 3 of your opponent's turns, destroy it during the End Phase of your that turn.

There's no real way to know what made Konami change the wording to this unless the company tells the players, anything else is really just speculation.