干父母 (if I may use this term):
干爹 = 义父
干妈 = 义母
so 干父母 = 义父母
but what does it mean?
English translations usually go like this:
干爹 = godfather
干妈 = godmother
义父 = stepfather (adoptive father/foster mother)
义母 = stepmother (adoptive mother/foster mother)
I'm not sure where all the different definitions come from but according to Chinese definitions they all just mean to formally acknowledge (拜认) someone as father or mother.
Wikipedia Godparent entry defines a godparent as:
In both Christian and secular views, a godparent tends to be an individual chosen by the parents to take an interest in the child's upbringing and personal development, and to take care of the child should anything happen to the parents.
Which doesn't seem to fit the above definition.
Adoptive / foster seems like it could fit - in specified situations but not as a rule.
What do these concepts equate to?