TL;DR: Should the description of the Scorpion Whip introducted in AP 151 Extinction Curse - The Show Must Go On have a sentence added to it to make it count as a whip for features such as Favored Weapon? Are there other weapons that should receive a similar treatment?
First off, I know that Favored Weapons aren't massively impactful to the game, even to the few classes that actually care at all about them. Secondly, I realize that the easy answwer to this topic is "Most GMs will probably say yes", but I think this discussion could be interesting anyway.
At no point in any of the rules text for deities or favored weapons is there a line that expliciotly states that the weapon named in a dietie's Devotee Benefits is refering to a single very specific weapon—however, that can be safely assumed since most times that's inherently clear. Cayden Cailean, for example, has the rapier as his Favored Weapon, and there is (AFAIK) only one weapon with "rapier" in it's name; that being the rapier itself, of course.
However, some deities can be a little more vague because there are multiple weapons that share part of their name. Erastil, for example: his Favored Weapon is the longbow, but there are two weapons in the CRB with "longbow" in their name: the longbow itself, and the composite longbow. For another example, let's take Ghlaunder, who's Favored Weapon is the spear—there are a great many weapons with "spear" in their name, the CRB has the spear itself, and the longspear.
Fortuantely, there isn't actually any confusion here. Even though no rules text about Favored Weapons specifically states that a deity's Favored Weapon entry is refering to one very specific weapon, this is made very apparently true when you read the description of the Composite Longbow, the last line of which states:
"Any time an ability is specifically restricted to a longbow, such as Erastil's favored weapon, it also applies to composite longbows unless otherwise stated."
That clears it up. From this we can assume that unless a weapon's description EXPLICITLY states that it counts as another weapon for weapon-restricted abilities, it cannot benefit from those abilities.
The only other weapon in the CRB (and the only other weapon I'm aware of at all) with that clarification is the composite shortbow, the last line of which reads "Any time an ability is specifically restricted to a shortbow, it also applies to composite shortbows unless otherwise stated."
The longspear doesn't have such a clarification, so a longspear will not benefit from any Favored Weapon features if your deity's favored weapon is simply "spear".
Fianlly, we get to the subject of the question: the scorpion whip, the description of which reads:
"A scorpion whip has a series of razor sharp blades set along its tip. Unlike ordinary whips, a scorpion whip doesn't have the nonlethal trait, making it deadly in combat but less effective when the wielder seeks to bring in foes alive."
Traits wise, a scorpion whip is exactly the same as the whip with only the following differences:
1) It has the uncommon trait.
2) It lacks the nonlethal trait.
3) it's bulk is L instead of 1 (even though it is just a whip with blades tacked on—if anything it their bulks should be swapped but that's not what this is about).
4) It's 5 sp instead of 1 sp (not that this is relevant).
Balance wise, I don't believe there's any reason to disallow the scorpion whip from being treated as a whip for weapon-restricted abilities. There are probably other weapons with similar cases across PF2E's many books, and there will probably be mroe cases int he future.
So should the line "Any time an ability is specifically restricted to a <weapon>, it also applies to <different weapon> unless otherwise stated." find its way into new (and errata its way into) more weapon descriptions?