The diapers that most hospitals use are Pampers Diapers.
Most hospitals use Pampers Baby Dry diapers or Pampers Swaddlers diapers.
Pampers brand diapers have been used by most hospitals for many years and even in the 1980s.
However some hospitals use Huggies diapers instead, but the majority of hospitals still use Pampers which are also good diapers.
For adult diapers, hospitals use some medical grade thin diapers that are basically like a napkin.
I was in the hospital before and had to wear an adult diaper for awhile and it was basically like a thin napkin.
Not sure what brand it was, but the diaper was basically useless.
But for babies and toddlers they get to wear either Huggies or Pampers diapers in the hospital, which are much better than the the adult diapers they supply for adults.