Let's break it down history-wise shall we?
1986- Super Mario Bros. 2 was released in Japan on the Famicom Disk Drive. After hearing consumer reports, claiming this game was "too hard" for their audiences, Nintendo of Japan felt the US Audience may feel the same way, so they underwent an entirely new version of Super Mario Bros. 2
1987- Doki Doki Panic (translation Run! Run! Panic!) was released in Japan on the Famicom Disk Drive. This quirky Arabic fairy tale, based on a Fuji TV cartoon show. Was the original game that gave the inspiration to our Super Mario Bros. 2. The main story focused on 4 characters trying to save their baby twins (Mama, Papa, Brother, and Sister)
Papa character turned out to be Mario, and the others Sister= Princess, Brother=Toad, and Mama= Luigi. The games are pretty much EXACTLY the same, except there is no run-button to hold down and the enemy and object sprites are totally different compared to ours.
1988- Super Mario Bros. 2 hits the USA, we were totally ignorant on what we had just recieved and loved/hated it to death, yet we are all guilty of playing it. Yet gave birth to the famous "MARIO MANIA" era of the late 80's. This is by far the most debated Mario game in history, next to Super Mario Sunshine on Nintendo GameCube in my honest opinion.
1988- Meanwhile in Japan, the Famicom cart Super Mario 3 was already released without us even knowing...good ol' marketing for the USA to keep secrets =)
1990- We finally recieved Super Mario 3 after a 2 year delay
1992- Back in Japan, after they discovered the USA had an exclusive Super Mario Bros. 2 edition the fans were jealous and demanded this game should be released! So it was released on Famicom cart under the name "SUPER MARIO USA". Which was silly to name, since many American ported games tend to get names like that, for example "Final Fantasy Mystic Quest" on SNES is called "Final Fantasy USA" in Japan
1993- Super Mario Collection (J)/Super Mario All-Stars was released in Japan and USA at the same time, Nintendo finally confessed what they had done for the past 9 years with the Mario series...
1994- A special edition cart of Super Mario All-Stars was released as a pack-in for people who bought the system bundle. If you find this baby, I'm sure you'll never turn off the SNES, has an orange label...It's an AMERICAN exclusive release btw..it's Super Mario All-Stars + Super Mario World....5 in 1 cart...the title screen even has Yoshi in the picture!