Bowser Jr.:
Bowser Jr. is the son of Bowser and prince of the Koopa Kingdom. First debuting in Super Mario Sunshine, Bowser tricked his young son into believing Princess Peach with his mother, setting him on a quest to rescue her from the "evil" Mario. After his and his father's defeat at the end of Super Mario Sunshine, he swore he'd get his revenge on Mario someday. He did fight him again in New Super Mario Bros., kidnapping Peach and fighting Mario in the towers of each world, and again fighting alongside his father. The father and son team were defeated, but it doesn't seems that they will give up anytime soon. Other than the main games, Bowser Jr. has appeared in several sports games. Mario Golf: Toadstool Tour, Mario Kart: Double Dash!!, Mario Power Tennis, Mario Superstar Baseball, and Mario Hoops 3 on 3 have all featured the young koopa prince.
Baby Bowser:
Baby Bowser is the Koopa King himself, Bowser, when he was young. He was the final boss of Super Mario World 2: Yoshi's Island. After his defeat, Kamek carried the young Koopa off into the night sky, vowng revenge. Baby Bowser did indeed get revenge in Yoshi's Story, where he stole the Yoshi's Super Happy Tree and turned the island they inhabited into a pop-up book, leaving only six baby Yoshies to stop him and save the island. He was again defeated. He next appeared in Mario & Luigi: Partners in Time. To be honest, I haven't played this game, so I don't have any good info to add. Sorry. Finally, he appears in Yoshi's Island DS, as a playable character in some stages and a boss later on.
