"Speak to" is slightly more formal than "talk to".
If - after the students have finished speaking to the principal - the principal told one of those students "Stay behind please, I wish to speak to you.", the student would be more concerned than if the principal said "Stay behind please, I wish to talk to you."
When a parent says to a teenager, "I need to speak to you" the teenager is in trouble.
Principals are not usually in trouble with their students, (the power in the relationship usually works in the other direction) so don't assume that they principal really is in trouble - they may just be doing all the talking.
* They are new and will have a lot of questions.
* There are several of them and only one principal - so they will be doing more talking.