As I understand it, each classic Super Mario platformer has these as their core themes:
SMB1: Alice in Wonderland
SMB2: Masks (from Fuji TV's Yume Koujou event)
SMB3: Japanese mythology
SMW: Dinosaurs
SML1: Ancient civilisations
SML2: Uhhhhhhh…… every wacky idea they had left??
I feel like all the sequels - 2, 3, and World - succeed at feeling like "a big adventure", but 3 and World both do so on a macro level, with the map screen and short one-note levels, whereas 2 is more "episodic", where each level is an adventure in miniature.