Hotspot: A particular active part of a fire.
Hotspotting: Reducing or stopping the spread of fire at points of particularly rapid rate of spread or special threat, generally the first step in prompt control, with emphasis on first priorities.
Uncontrolled Fire: Any fire which threatens to destroy life, property, or natural resources, and is not controlled by crews.
Contained/controlled/extinguished: While these terms seem interchangeable, they have three specific meanings.
Containing a fire: A fuel break around the fire has been completed. This break may include natural barriers or manually and/or mechanically constructed line.
Controlling a fire: The complete extinguishment of a fire, including spot fires. Fireline has been strengthened so that flare-ups from within the perimeter of the fire will not break through this line.
Extinguished: When all hot spots of fire are completely out. Since hotspots can burn for months after a fire is controlled, and it can be difficult to know when all hot spots have cooled completely, information on when a fire is extinguished is not tracked.
Information from the National Park Service.