You are correct they both mean happening because of good luck. Fortunately more precisely means happening because of a fortunate event. Luckily more precisely means because of a lucky or good event. If you find a $1,000,000 dollar bill in the street that is lucky. If you find a $1,000,000 dollar bill in the street because something happened to make you change your usual or planned route. That is fortunate. And also lucky. If you loose a $1,000,000 dollar bill on the street that is unlucky. If you loose the $1,000,000 dollar bill because you put the money on a horse hoping to double your money, and the horse looses the race. That is unfortunate. If the wind blows the bill (bank note) out of your hands that is unfortunate and unlucky. If the bank does not change the bill because there is no such bill in circulation that is unfortunate and stupid on your part. If you are able to sell the $1,000,000 dollar bill that is very lucky on your part. If the $1,000,000 dollar bill is a bond of some kind and not protected in any way and you are legally able to collect the $1,000,000 dollars that is extremely fortune. And you are extremely lucky In all cases there is an element of luck and bad luck (being unlucky) and also fortunate (being fortunate and unfortunate)

“fortunately” is a slightly higher level word then “luckily”. To me “fortunately” sounds better for things that are bigger. “She got married when she was 17 to a man she had never met. Fortunately they made a perfect couple and went on to live an extraordinary life together” “Her car broke down on the country road. Luckily someone came by a few minutes later and gave her a ride to town.”

the meaning is the same actually, but fortunately is more formal :)

i use them interchangebly

there is none i think.