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Adventure Island (アドベンチャーアイランド), released in North America as Dragon's Curse, is an adaptation of Monster World II by the same developers. That means it's related to Bikkuriman World and The Dynastic Hero.
Never mind the bizarre "Adventure Island" brand for the Japanese release, Japan even got this version before any version of the original Monster World II, due to some unfortunate circumstances. On the other hand, this version managed to come out before Monster World III, so technically Japan got the games in order...
Because of the hardware jump, Adventure Island is a big improvement over the original Monster World II. The relationship is very similar to the two versions of Monster World III, but in reverse.