I'm not sure about the original question as to whether children learn differently from adults. I tend to think not. I think that there's probably some kind of baggage that children don't have compared to adults, and that's a psychological thing.
Let's not forget that out of every child who takes up the piano, very very few of them are going to become competent. Most are going to get through the first beginner book and give up, some will get to the end of the second beginner book, and others will embark on a study of grade exams. Out of those who start grades, the average I've noticed is to get to about Grade 3 ABRSM and stop. Some decide to go to Grade 5 and stop before they have to sit a theory exam. Very few will ever get to Grade 8 and so they think it's this kind of mythical place that only superstar pianists get to (if only they knew...).
Out of those who get Grade 8, very few of them will think about auditioning for a place at music college, and even fewer of them will get that place. Those who get in to music college could pretty much hold their own in a recital and concerto at least by the end of the second year. I'm not saying they'd sound like Yuja Wang, I'm saying they'd give a respectable performance with everything dialed in. That's not the same as sounding like a concert pianist, but it's a very good start.
Anyway, back to the child beginner, most of them learn really slowly, and most of them don't display what would be considered "talent". That's fine because for me it's not about "talent", it's about a process of learning and putting in the work to get the result. Even the most "talentless" students will learn to play well if they put in some work. But it takes a long time. And that's OK. I use quotation marks because I don't like the terms "talent" and "talentless" in most situations. There are obviously those who have inborn talent - Martha Argerich playing Beethoven 1 at 7 is a good example of that - but for most people it's about enjoying the process of practice and seeing the result.
I think that adults as long as their hands aren't arthritic or injured might have certain advantages over children. The biggest one is that they're doing it because they want to do it, and not because someone else is telling them. Also, I believe there are adults that have that same aptitude as some of the "talented" children but it might not have been tapped.
I would like to see us get away from the idea of (and the selling of) child prodigies, honestly. Ranjit you said to me that shouldn't we regard a late starter who goes from learning the basics to playing Liszt in a matter of two to three years as a prodigy in the same way as we would a child? Yes, we should. I don't believe there should be barriers to learning or even presenting a professional recital based on age if someone has the time and the will to practice. The industry itself doesn't really allow for it because the major competitions have low age limits. I do think 35 is a low age limit because sometimes even a talented pianist who's had a fine technique for decades doesn't really get to grips with it until they're 40.