Baby Mario is Mario from the past, when he was still a baby. He appears in some videos of SuperMarioGlitchy4. He and Mario seem to be separate persons in SMG4's bloopers, as in the video game Mario & Luigi: Partners in Time on Nintendo DS.
It is shown in Luigi wants to build a snowman, that Baby Mario is shown to be enjoying his time with Baby Luigi (as Luigi said in the video, they used to be best brothers), except for the picture of Baby Mario trying to kill Baby Luigi with a flamethrower.
Baby Mario was one of the Marios residing in the Grand Mario Hotel. He was one of the few Marios not to be aggravated by Mario when he ran the Mario Hotel, and seemed to enjoy his older counterpart's company.