Is there such thing as ER Surgeons? or is there just trauma surgeons and ER doctors

Yeah no such a thing as ER Surgeon.

There are ER physicians but they are not surgeons. They triage, diagnose and treat patients. They occasionally perform some minor procedures such as suturing lacerations, drain abscesses etc.Depending on what they find, they may then ask for the help of various types of other medicine doctors or surgical specialties.

ER physicians generally don't perform higher risk surgical procedures such as tracheotomy, chest tubes etc unless there is no one around who is more qualified to do it.

In the case of trauma, since time is very critical, general surgeons with expertise in trauma (aka trauma surgeon) are often in the ER to help the ER physicians.

Depending on the severity of the trauma, other surgical subspecialties such as neurosurgeon may be present in the trauma bay as well to deal with brain trauma. Head and neck surgeon may be there to deal with facial injuries or airway issues. And orthopedic surgeon may be there to deal with severe or urgent fractures.

Emergency Medicine: Medical Physician
Emergency Surgery/Trauma: Surgeon. Some also pursue a Trauma Fellowship after regular Residency in Surgery.

ER physicians are NOT surgeons.

Trauma surgeons and general surgeons routinely evaluate patients in the emergency department.