Does society treat miscarried/stillborn babies differently than infants that die after birth? (Please read details)

I decided to ask this question after seeing a profile on Facebook which had the profile picture set as an image of the woman’s premature stillborn infant. At first the image made me uneasy, but I had to take a moment to ask myself why. Was it because looking at a deceased child is unsettling, or was it because the baby was essentially never born?

In another instance, I happen to know a person that unfortunately miscarried and opted to keep the remains in order to hold a burial service for the child. (I can’t recall if it was technically a stillbirth or miscarriage, but the baby was relatively well formed -though tiny.) She kept the child in her home until arrangements could be made for a small service.

Word gets around, and many people voiced their opinion that what happened was horrifying to them. Some of the things that were said about the mother were shocking and sad, people used words like “sick” and “disgusting” to describe her choice. However, if you surrender the remains to a hospital it will be incinerated as medical waste.

From the mother’s viewpoint, as a person that wanted the child, I can imagine it would be difficult to let go of your child as “medical waste.” Also, to the best of my knowledge, other arrangements are difficult to make when the child is miscarried or stillborn. Since I am technically asking multiple questions here, I’ll lay them out individually:

1.) Does society treat these cases differently from those when a child is born and then passes after birth?
2.) Can the mother/parents of a stillborn or miscarried baby make arrangements with a funeral home that are identical to that of a child that has died after birth? Or is the only option to take the remains home or have them incinerated by the hospital?
3.) How do you feel personally about someone openly mourning the loss of a child if the child was not born before dying? How do you feel about a Facebook photo of a stillborn fetus vs a photo of a child in a coffin taken by the funeral home? How do you feel about keeping remains in a freezer or similar circumstance while preparing for a service?

Any other thoughts on the subject are welcome.