Are theere different fields of anesthesiology?

Yes. Pain management critical care medicine palliative care cardiac anesthesia pediatric anesthesia neuroanesthesia obstetric anesthesia.

Anesthesia fields. There are several but not all have subspecialty boards or fellowship programs Trauma/Transplant Regional Anesthesia Orthopedic Cardiac anesthesia Obstetric anesthesia Pediatric anesthesia Neuroanesthesia Critical Care Pain Management.