Bill, CFDMarshal, anesti, and Rodent251 are all correct.
The definition of a Task Force from the LAFD's website:
http://lafd.org/apparatus/111-fire-a-rescue-resources/295-lafd-task-force
From my knowledge, a "Task Force" in L.A. is made up of 3 pieces of apparatus, the Engine Company, the 200 Series Pump Engine Company, and the Truck Company. For example: Engine 27, Engine 227, Truck 27. When responding as a "Light Force", the main Engine Company is not included in the response. A Light Force in L.A. consists of the 200 Series Pump Engine and the Truck. For example, Engine 227 and Truck 27.
A little history. Task Forces originated during the Watts Riots of the 1960's. Department officials determined that it was safer and more effective for multiple pieces of apparatus from the safe fire station to respond together, especially in tougher neighborhoods. Also, more apparatus responding from the same fire station meant that other fire stations didn't have to be tied up at the same fire or incident. Basically, one fire station could handle your average structural fire by itself. Thus, there wasn't any 2nd or 3rd due units, just a Task Force from one station, accompanied by a Battalion Chief. Prior to the Task Force, fire stations only had either 1 Engine or 1 Engine and a Truck in the same firehouse. With the Task Force initially came what is known in NYC as "Second Section" companies. On June 1st, 1966, Heavy Duty Task Force 9 was organized, becoming the first Task Force in the LAFD's history. When it was first founded, a Task Force, or Heavy-Duty Task Force as it was initially referred to, consisted of 4 pieces of apparatus, the Engine (or Triple Combination Pumper, Triple for short), the Wagon, the Pump, and the Truck. The Engine was the backbone of the Task Force, and had a pump, hose, and a tank. The Wagon I believe also had a pump, hose, and tank with the addition of either a Telesquirt or Snorkel device. The Pump only had a Pump and extra equipment, possibly with some 3" supply hose. The Truck was your standard "Truck Company" by definition, and always a tiller, as they still are today. At first, there were only a handful of these "Heavy Task Forces".
Here's a picture of "Heavy Duty Task Force 3" in Downtown L.A.
And "Heavy Duty Task Force 9", the city's first Task Force. Note the Snorkel for Wagon 9.
And "Heavy Duty Task Force 9" in the early '70's, after the Snorkel for Wagon 9 was replaced by a Telesqurt device.
Originally, Task Forces were staffed by anywhere from 15-18 men. Eventually, many fire stations across the city had Task Forces, only without the Snorkel or Telesquirt 3rd Engine. Only the original "Heavy Duty Task Forces" had those. As the '70's progressed, so did budget cuts. Manning was gradually cut from the Task Forces. Eventually, the "Wagon" piece was dissolved, meaning no more Snorkels or Telesquirts. The Heavy Duty Task Forces that had consisted of 4 pieces were cut down to 3 pieces like the rest of the Task Forces throughout the city. Thus, Task Forces were now comprised of an Engine, a Pump, and a Truck, which they still are today.
Here is the original "Task Force 10" from the early '70's. Note, only 3 rigs and no Snorkel or Telesqurt.
When these 3 pieces of apparatus respond together as a "Task Force", they are staffed by 3 FF's and 1 Officer on the Engine, 4 FF's and 1 Officer on the Truck, and 1 FF on the 200 Series Pump Engine.
The 200 Series Pump Engine is basically a supplemental unit, or secondary unit for either the main Engine or the Truck, depending on what the response is. The 200 Series Engine, I believe, carries less equipment than the main Engine.
Today, when responding as a "Light Force", the 4th firefighter from the Truck jumps on the 200 Series Pump Engine, to make it 3 FF's and 1 Officer on the Truck and 2 FF's on the 200 Series Engine.
Very rarely does the Truck respond by itself. It is almost always accompanied by the 200 Series Engine. Likewise, a 200 Series Engine always responds with the Truck and never by itself, similar to Chicago's Squad concept. Therefore, a Light Force is considered one "Company" in the East Coast vernacular. Thus, a Task Force is comprised of two "Companies", the Engine Company and the Light Force.
Additionally, while a Task Force responds to calls like a Structure Fire or serious MVA, a Light Force may respond to calls such as an Elevator Rescue or minor MVA's. A Task Force can be comprised by units from two different fire stations, depending if an Engine or a Light Force from one station is unavailable.