No, they don’t mean exactly the same thing. To “fare well” just means to do well, either in a task, one’s maturity or in a career. It’s where we get the word “welfare”.
– “His music career was not successful in the United States, but he fared much better in Japan.” (True story of one of my sister’s classmates.)
– “The new law didn’t fare well with the public, so the legislature quickly repealed it.”
To “grow well” means literally to grow well. We use it about things that grow. We can say that plants aren’t doing well, faring well or growing well, but only “grow” really means grow.
I have seen an American book called “From Welfare to Faring Well”. You could translate it from English into English as “From Public Assistance to Prosperity”. It’s about a man who started adulthood depending on free money from the government, but he started to rely on himself and got rich.
Yes, it does.
Now that I have read Jamie’s explanation, this is how I understand it:
Crops/plants fare well – they develop sufficiently; they bear/produce fruit; the amount of grain, fruit etc that is grown in one season is a large one (the harvest is very good) and the quality of the fruit, grain, flowers etc is good.
All that as opposed to:
Crops/plants fare badly – they develop insufficiently; the amount of grain, fruit etc grown in one season is poor (the harvest is bad) and the quality of the grain, fruit etc is bad.