What are the differences between different mental health professions and who is best suited to help kids?

It depends on. The problem. In general, a child should have an evaluation by a child and adolescent psychiatrist to rule out illnesses that could require treatment with medication. The psychiatrist may then recommend a psychologist or therapist for the talk/play portion of the treatment.
Providers. The pediatrician is your primary care doc who can refer you to different specialties. A child psychiatrist also grad from med school, and had a 5+ year training in mental health eval and treatment and can prescribe meds and screen for medical problems. Psychologists have either masters or doctorate in psychology can do cognitive testing and therapy. I believe its best to have coordinated care.
Pediatrician. I have always believed that the 1st place to start is the trained pediatrician.They are able to triage the problem and find the best source of help.Different providers have different levels of experience and areas of expertise.