To be “on the team” or “in the team” (you can use either) means to be part of the team (ser seleccionado para el equipo). To “make it onto/into” the team means that you were selected to be a member of a team, for example in a football team the manager or coach decides who will play in the next game. So if someone didn't make it onto/into the team, it means they were unsuccessful in their attempt to be part of the team. You could also use it to refer to other things, such as universities (“I didn't make it into the Universidad Autónoma de Madrid, however I made it into Complutense”) or transport (“I didn't make it onto the 17:45 train from Atocha but I made it onto the next train at 18:15”). It means you were unsuccessful in an attempt to do something.

It concerns the selection for a team in sport. So getting onto a team is competitve and you are not always selected to play.

Thank you Steve

"Make it on" sounds like it might be a phrasal verb. If it is, then "make it on to the team" is correct, not "onto". :)