Well I look at it like this:
-Napalm is good for "open air" DZ's. Meaning forested areas, low obstruction, etc. Low cost and simple to mass produce. Can only really be dropped by aircraft due to its weight. Good against most medium structures and defenses. Burns very hot.
-White phosphorus is good for "urban" DZ's and areas with obstructions (ie: areas with built-up infrastructure). Its more an "area denial" munition than anything. A bit more costly and harder to produce. Can be fired from artillery, dropped, or even used in hand-deployed forms. Burns EXTREMELY hot. WP is a more refined and volatile munition than napalm. We've pretty much 100% moved to WP as a primary incindiary.
In modern napalm munitions (mostly used now to clear land), WP is added to increase burn rate and effectiveness. So to be honest, they're less of two different munition types than components in a singular munition.
Napalm's earliest form was litterally just gasoline with off the shelf Jello mix packets poured in.
Someone correct me if I have my facts mixed up.
Incidiaries are not meant to "catch the enemy on fire"...its meant to destroy structures and clear forest. WP's primary uses nowadays is to mark artillery targets (they fire WP shells first, then roll live).