Examples, not sure how to explain well and my brain is fried.

Brother or sisterhood is used:
I felt a strong sense of sisterhood with Angela, even though we’d only worked together a few times, she understood my uphill battle with corporate.

Friendship:
Our entire friendship was based on her needing something and I provided it. Destructively symbiotic.

@KNOWITALL I guess they’re the same.

“Ship” when it’s close and personal, singular somewhat. (As in “kinship.”)
“Hood” when it’s like a gang or club, plural somewhat.

As in da Hood

@kritiper I think the singular or plural is correct, but the “close, personal, gang, club” parts don’t seem to hold true. Counterexamples: craftsmanship, marksmanship, personhood, womanhood

There are no rules.
It is arbitrary, so you better memorise every case separately.

’—hood’ generally denotes belonging to something, “Neighborhood” is an example. It is a place where you and your neighbors belong to.

”-ship” is the condition of being something. “Friendship” is the condition of being friends,

@Zaku Yes, hence my somewhats.

Yes—kritper said it first