Wow... this is WAY better than the first Monster World game... For one thing, money isn't limited anymore so you can actually save up and buy all the best equipment in the game. The exploration is similar to the first game, but it's somewhat easier to backtrack and see what all the different paths lead to now.
I started playing the Turbographx-16 port of this game, which seems like the definitive version since it has save files. (EDIT: This is no longer the case, the definitive version is now the HD remake on Steam/Switch)
It starts right from where Wonder Boy in Monster Land left off... In fact the first part of the game is kind of a redo of the final part of the previous game.. after killing the Meka Dragon, Wonder Boy gets cursed and turns into a Dragon. Then you escape the castle and enter the town where the real game begins...
I played all the way through up until I defeated the 2nd boss and transformed into the "Mouse-Man" form... I can now walk along certain walls and ceilings and get through small passages that I couldn't before...