Yes they are have a close meaning , and similarities :- e.g.
As MatrixGyal said about the Question: '' How are you /How do you do /What you doing,..'' May you Answer with Good / Fine or even well. I think the most better and strong in its meaning here well and Fine , rarely to you nice so weak.
In Another Example: If somebody ask you about : '' Do you Speak English?'' Then its Answer the most perfect and true in meaning and Grammar '' I speak English very well'' =Means in the perfect way , You Cant answer with any other of '' Good/ Fine or Nice'' its Wrong .
Well sometimes mean '' Yes , I agree , OK,... and also Fine may use at the same way '' But the others don't work at the same way .
Nice may yous for both '' Man , and Animal'' Nice boy , its a nice cat '' , But Good its mostly uses with man.
Also Good uses when someone do a Good Job we says '' Very good = well done= Good Job'' we cant say very well in this case its wrong.
Thank you ^_^