Yeah, it's complicated...
Yoshi's Island isn't Super Mario World 2 in Japan, it's just "Super Mario: Yoshi's Island". I think it was SMW2 for a marketing push in the West.

And SMW was initially "Super Mario Bros. 4: Super Mario World" in Japan, so all sidescrolling mainline Mario games are "Super Mario Bros." titles in Japan and Yoshi's Island isn't.

It's part of the Yoshi series for me and Yoshi's Story is the sequel (without Mario). Or do you consider Yoshi's Island DS as the first sequel?











