Both come from Latin.
The noun amicus(friend) from amo(I love)
The verb affor(to address) from ad + for(to speak to)
I am pretty sure etymologically amiable should be much more warm, pleasant and friendly. Amiable should be closer to friendly. While Affable should be closer to easy to talk with.
Nonetheless a Semantic change/drift might have occured.
What is the difference in nuance of amiable and affable?
A possible answer to my question could be given by Jim's comment.
If so I would need a confirmation of whether amiability(amiableness) is the active/intent desire to please while affability(affableness) is the passive condition of actually pleasing regardless of any will to do so.
Best Answer
I don't know where you got the etymology from but Etymoline says
In fact, the meaning I have emphasised was preserved in the modern use of the word:
Cambridge defines affable as meaning
And AHD says
(The same reference to speech is present in ineffable - which cannot be spoken, indescribable)
Amiable is more commonly used than than its other variant, amicable and than affable. Etymoline says about it:
Cambridge defines it as
and AHD as
There is definitely an overlap between the two in use, they can both mean pleasant and friendly, but these definitions show amiable to describe someone or something that is likable (easy to like), whereas affable someone or something that is approachable (easy to approach or talk to, therefore welcoming).
Having said all that, here is what a native speaker said about this issue on a forum