The People: No Different Flesh, by Zenna Henderson (1967.) This is her second collection of "People" stories, and the third of her 4 primary collections - those which collected her stories for the first time.

No Different Flesh
Deluge
Angels Unawares
Troubling of the Water
Return
Shadow on the Moon

These are from Magazine of F&SF - from 1961 to 1966. The sequence is changed from magazine publication order, and there are some untitled/unmarked connecting interludes at the end of most stories.