Compare and contrast the use of WP in Fallujah to a generic chemical weapon.

A chemical weapon when deployed will retain its toxicity in vapor or liquid form for a variable length of time usually measurable in hours, depending on the agent. This is to create wide and indiscriminate dispersal.

WP oxidizes spontaneously and does not exist in a residual form when exposed to oxygen other than smoke, which is no more harmful than any smoke because it is no longer "white phosphorous" having oxidized. In addition, the military application in question uses WP embedded on felt wedges to allow a more controlled dispersion versus indiscriminate.

Chemical weapons require protective equipment and decontamination to operate in the affected area.

WP requires none after it oxidizes.

Chemical weapons attack the body in a variety of ways including inhalation and absorption through the skin to produce a toxic effect.

Though you can replicate a scenario in a controlled environment that may demonstrate this for WP, such as forced ingestion, the practical application of WP weapons causes injury by the heat generated by oxidation. The injury is localized to the exposed area and does spread through the body, but it would take massive amounts of exposure to become toxic, which is impractical to this application. It continues until the WP is removed, oxidized, or removed from oxygen. This is a burn, not a toxic reaction.

If you are in a location attacked with a chemical weapon, there is no way to avoid it without protective equipment.

Falling WP can be avoided easily with cover. The WP may cause secondary fires and associated smoke, but fire and smoke are not chemical weapons.

The lethality is what really shows the difference:

If you deployed a chemical weapon against a building containing 20 enemy soldiers, they would probably all die and any one near the building, down the street, around the corner….

If you deployed this application (base-ejecting, artillery 155mm projectile with WP embedded on 116 felt wedges with a total payload about the size of a coffee can) against a building you would have a very low probability of killing any of the soldiers. You would even have a low probability of injury, since in this scenario the enemy has cover. You may get secondary effects from fire and concentrated smoke, but this is not a chemical attack.

Chemical weapons have one function: kill everything in the affected area.

WP has other functionality such as obscuration, incendiary, and marking a target.

Note: Since writing this I learned that WP mortars were used in Fallujah though not shown in the RAI documentary. The net effect would be more dispersion over a much smaller area of about 20 meters. The mortars were used when HE or bullets could not penetrate in order to drive the enemy out with smoke and fire, the secondary effects. Since HE could not penetrate it is unlikely WP could penetrate and unlikely it made direct contact with combatants or "civilians" who might be inside.