adopt vs foster

Is there any difference between ‘adopt & foster’ or they are synonyms?

When adoptive parents adopt a child, they take legal measures to have the child officially declared to be their own son or daughter. The child’s legal status is then the same as that of their natural-born child.

When foster parents take in a foster child, they are just caring for the child temporarily (sometimes for years) on behalf of the state. Usually this is a child who has been removed from his real parents’ home by the courts due to some crime or unhealthy environment in the home. If the parents improve their behavior, the child may be sent back to his parents, but it’s also possible that he will stay in foster care (with one family or a series of families) until he is 18.

After fostering a certain child for a while, some foster parents develop such a good relationship with him that they decide to adopt him.

However, fostering and adopting are not the same thing. Foster care is common in states (like mine) that have no orphanages.

Can a younger person adopt an older person?For exmaple, a 30-year-old man who adopts a 50-year-old lady to become like his own mother.In other words,he would say that she is his adopted mother or godmother?

Not legally, Wong. Adoption or fostering ends at the age of 18.
I have a wonderful mother with whom I have a loving relationship, but when she was alive (she dies all too suddenly and tragically of cancer a few years back), my best friend’s mother used to describe me as 'adopted daughter" to everyone. I, in turn, referred to her as “My adopted mum”, or “my second mum”. It was simply a term of endearment indicative of how close we were though. (And my own mother understood the relationship and endorsed it.)
Because of this, you post made me smile, though the smile was tinged with sadness.

THANK YOU for such a detailed explanation. Now I understand the difference. And you know, I just realised that I can’t translate ‘foster’ into my mother tongue, because we don’t have such a process in Ukraine. So the word ‘foster’ belongs to the words we define as realia.
Many, many thanks!!!