Is there a difference between these two words, and if yes, what?
The question arose while I was talking with my German-speaking friends during lunch, and they argued that "gelungen" doesn't have a translation in English.
"Gelungen" ist the participle of "gelingen" and has a straightforward meaning of "been successful" - Just like "erfolgreich".
Gelungen does, however have a less straightforward meaning that becomes obvious in
ein gelungener Abend
eine gelungene Aufführung
which cannot simply be be transported by translating to "successful". Here there is a connotation of overall having been interesting, entertaining, or otherwise just generally "perfect" in every aspect (which IMHO would be the closest translation of this connotation - I thus seem to disagree with your friends). This obviously goes beyond simply "succeeded" as that would apply to one single definite target only.