A Klassenlehrer is a teacher who supervises one particular class over a couple of years. His tasks are somewhat similar to those of a homeroom teacher. He teaches more than one subject to his class. He is the first person a parent should approach if there is a problem. The Klassenlehrer will then investigate the problem and report back to the parent.
A Vertrauenslehrer is a teacher who acts as an advisor and arbitrator to kids, particularly when they have problems with other teachers. Vertrauen means trust in German, and the Vertrauenslehrer must keep such information confidential. Encourage your kid to speak to the Vertrauenslehrer, when things go wrong. Most have a genuine interest in children and do a good job.