Interesting, but it confuses me a bit.

Ambidextrous means: "that the person has no marked preference for the use of the right or left hand".

Unlike what is normally assumed, it doesn't mean you've mastered both hands, it doesn't imply you can write equally well with the left or the right, but that you could have just as easily learned either. You had no marked preference when you picked up the activity initially.

Cross-dominance seem to imply there was a marked preference, but that it is the left or right hand differs per activity.

That said, I wonder if they're really the same. Often people say ambidextrous as you are equally good with both hands, which would always require practice on both side. But maybe cross-dominant people can equally learn?

Under that reading, cross-dominance could be what ambidexterity actually looks like in practice. If you genuinely have no preference, there's no reason you'd consistently land on the same hand across all activities, you'd be influenced by context, who taught you, which hand was free, etc.

Have you ever tried your other hand at activities? And are you surprisingly good with it, even if not as good? I tend to be better using my other hand at most things than say a fully right handed person, but never as good as the hand I've been using for that activity consistently.