Undocumented is the much broader term which doesn't carry the negative connotation that somebody living here is an "alien". They may have come here illegally, or their status may be in limbo, they could be a refugee seeking asylum, they could have overstayed their visa, they could be waiting on a ruling from an immigration court, or waiting to appear in court.

The administration could have decided to revoke their status. A judge could have put a stay in place because deportation would mean returning them to a dangerous situation. See the Abrego Garcia case. Some don't even know their status since their parents brought them here at a young age.

So you see it's not as simple as branding everyone an "illegal alien". That's political propaganda at work.