Difference is as far as we know the first family did everything legally and tried to find her a new family who could take care of her needs when, for whatever reason, they decided they were ill-equipped. They paid for her to be seen at a world renowned children's hospital so it's possible she got some of those recommended treatments. We can see from photos (and from Michael's statement that she ran towards them when they met her) that she had corrective braces fitted before she went to live with the Barnetts. The Barnetts, on the other hand, went out of their way not just to deny appropriate medical care when they had custody of her but to deny her any chance of ever getting the medical treatment she needed. They deliberately took steps to prevent her from accessing support networks and left her in an unsafe environment where she didn't know anybody. I think the woman who found her said she didn't have shoes on so I doubt they were keeping up with her physical therapy/castings. They expended plenty of effort trying to get her committed to psychiatric facilities, however. They were making out to everyone that they were given no medical information about Natalia even though she had extensive records and they were in possession of a surgical timetable from the Boston doctor (I'd actually bet money she shredded them). They were telling the Indiana doctors she had a different form of dysplasia and no doubt were withholding those medical files from them so they had to treat her like a blank slate. That would slow down treatment considerably and prevent doctors from giving the best timely care and advice.
I wonder if they had life insurance policy on her. They're stupid and evil enough to have done that.