I might be able to jump in here and offer some assistance.
Genearally speaking, the difference between a Fire Investigator and Fire Marshal are distinct. A Fire Investigator stricitly investigates the cause and origin of a fire, where as a Fire Marshal investigates the cause and origin and does inspections and enforcement. The titile of Fire Inspector generally relates to persons hired by Fire Dpeartments who inspect buildings for fire code compliance but have no enforcement authority.
Now the above is not always the case. Throughout different parts of NYS the titiles have been diluted.
The Fire Investigator does just that, and investigates fires. You can work for private or public agencies. Mostly through upstate they have volunteer fire investigators and teams, some of who have law enforcement status (peace officer). They usually work closely with the local police to help with prosecution for criminal cases. Depending on the jurisdicition some fall under the county fire coordinator, which can authorize those persons for red light use (from what I understand).
The Fire Inspector usually works for a Fire Department doing routine fire inspections. They usually have no enforcement power and serve more of a pre-plan function for the Fire Department. Now in Nassau County, while they are called Fire Marshals you are hired under the civil service title of Fire Inspector. Nassau also has certified "assistant fire inspectors" which are appointed to work at local fire departments (which have no enforcement power).
In Suffolk County the County, Towns and Villages all employ fire marshals, which generally do investigations and enforcement. There a Fire Inspectors that work for local fire departments (no enforcement authority).
In NYC there are many levels of this as well. There is a Fire Marshals office, who are NYC Fire Fighters. By test you are appointed a Fire Marshal with police powers. They have a Bureau of Fire Investigation (BFI) that does cause and origin. They are other branches that doe inspections ans enforcement. Additionally, regualr fire fighters do routine building inspections (BI's) and there is a separate Fire Insepction unit with a separate titile and civil service test (not fire fighters or peace officers).
The NYC police department has the arson and bomd sqaud (A+E) that work with the Fire Marshals in large scale fire scenes. Generally they handle the bombings and other crimes.
Also, NYC Fire Marshals have much broader legal authority as regualr police officers to do there jobs, which is given to them by city law and charter. They also have specialized units like the Social Club Task Force.
Generally Speaking, the Fire Marshal position is a civil service test/title and is a law enforcement job.
Hope this helps some.....