From a firefighting perspective, there are two broad types of unwanted fires.
Structural fires and wildfires.
As a rough rule of thumb, structural fires occurring when a building is burning.
These tend to be more urban and occur in areas where people inhabit.
Conversely, wildfires refer to fires that occur in rural areas that have fewer people and are sometimes called wildlands (hence wildfire).
The Wikipedia article on wildfires provides a nice overview.
Forest fires are a type of wildfire that many people use as a synonym.
The reason firefighting splits the two types of fires is that they require different gear types to fight and use different methods.
Also, many (probably most) firefighters are only trained to fight structural or wildland fires but not both.
Wildfires are also closely related to controlled burns, which can be done as a land management tool.
A controlled burn that gets out of hand can become a wildfires.
Conversely, controlled burn can be used as a tool to fight wildfires.
Also, wildfires are sometimes left to burn in either remote wilderness areas or managed areas that where scheduled to be burned.
Personally, I received wildland firefighting training in college to help out with controlled burns, which gave me my perspective to answer this question.
We were taught explicitly that we were not qualified to fight structural training.
The US Forest Service has a career webpage for people interested in more details about this training.
Also, sorry but I cannot help you with your meta-question.