I'm a native U.S. speaker. In my opinion, there is no difference in meaning. (But perhaps Naomi is more careful about usage than I am). After recovery, I do not think there is any difference in meaning between "I'm well," "I'm better," and "I'm all better."

There is a slight difference. If someone broke their leg, to be more specific, I would say, "I hope that gets better soon". Something broken, damaged or bruised needs to be repaired or made better. If someone had a cold or the flu, I would say, "I hope you feel well again soon". The word "well" has more to do with "well being". Hope this helps

They are the same. Both are used interchangeably :)

I think both are workIng but. Better soon. Would be better :)