Okay, they cheat us. Here's how sizing works.
If YOU try on your daughter's shoes I bet you can wear them right? That's because they make kids shoes differently.
I wear a ladies 7-7 1/2 and I can easily wear a girls size 4 and 4 1/2. WHY? Because the people that make kids shoes make them differently. They know that mom's want their kids to stay kids for as long as possible. So they enlarge the sizes and keep the kids shoes looking like little girl shoes and don't make them hoochie mama shoes.
If you go to an adult shoe store and look at the smaller sizes you'll see that an actual adult shoe in a size 4 is a tiny heel or adult style shoe and it will not fit your daughter in any way. It would be totally too small, narrower, and more tapered to fit an adult foot that is shapely and not growing any more.
The same thing goes on with clothing.
A GIRLS size large is about the same size as an adult small. Sometimes it could be the same as a medium.
Girls size 8/10 or 10/12 are the same sizes as an adult x-small or small. A girls pre-teen will swallow a lady that wears a small too. It's more like a medium or even a small running ladies large.
Think about the measurements. A kid might have the same size waist but they DO NOT have the breasts or hips of a woman who has had a child. So adult clothes MIGHT be more thigh high cut, lower neckline, larger arm holes, etc....a child's garment will have more modest lines and will probably have narrower hips. This is what used to be called a Junior size. They had smaller bust measurements and smaller hips. They were odd sizes like a 3, 5, 7, 9, 11, 13, and so forth. They were made to appeal to younger kids and very young adults.
Where women's clothing were even sizes and had a fuller breast area and fuller hip line. More of an hourglass shape. They were sizes 2, 4, 6, 8, 10, 12, 14, and on.
The garment industry doesn't hardly do this type of sizing anymore though. They do sizes like 9/10, 3/4, etc....
So even though your daughter wears a child's size 4 shoe that means she has about a size 6-61/2 foot.