I found something within the Summon monster entry on d20pfsrd which doesn't match something on the same page.
Near the top
When you use a summoning spell to summon a creature with an alignment or elemental subtype, it is a spell of that type. Creatures on Table: Summon Monster marked with an "*" are summoned with the celestial template, if you are good, and the fiendish template, if you are evil. If you are neutral, you may choose which template to apply to the creature. Creatures marked with an "*" always have an alignment that matches yours, regardless of their usual alignment. Summoning these creatures makes the summoning spell's type match your alignment.
At the bottom
* This creature is summoned with the celestial template if you are good, the entropic template if you are chaotic, the fiendish template if you are evil, or the resolute template if you are lawful; you may choose any if you are neutral.
It looks to me like there are more templates possible depending on your alignment in this bottom wording.
When I went and checked my physical core rulebook, the top wording appeared in both top and bottom. Was there an update or errata for the bottom section, one which was never applied to the top?
Best Answer
No.
Not an errata, but those templates came after the Core Rulebook and Bestiary were released. On Bestiary 2 to be exact (pages 292 and 293), which stated that they could be used on summons, but did not say how they could be summoned with the templates.
Cool, so we can summon monsters with those templates, but how exactly do they work? No rules were given on the Bestiary 2, and we still had no rules saying how they worked by then.
Do we apply entropic if we are chaotic, and resolute if we are lawful? What happens if we are lawful good, does the creature obtain both resolute and celestial templates?
Later, on the Monster Summoner Handbook, we got a further expansion on those templates, with some archetypes allowing you to summon only entropic or resolute templates and feats that allow you to apply different templates to the creature summoned.
And added a bunch of new templates based on elements, such as aerial, aqueous, chthonic, dark, fiery, and primordial templates.
Considering that the archetypes restrict your summoning and the templates available and add more options, but does not allow a caster with no archetype to summon creatures with those templates.
Herald Caller Archetype
The Herald Caller (Cleric) archetype from the Monster Summoner Handbook is important because he has abilities that affect summoned monster's templates.
Meaning that those templates could not be normally applied to summoned creatures. And this also doesn't contradict the previous text from Bestiary 2.
But it allows the caster to be of a neutral alignment, follows an aligned deity, and still be able to summon an entropic or resolute creature. Example: A neutral good follower of Saerenrae (lawful good) would be allowed to summon resolute creatures.
Asking James Jacobs (Paizo's Creative Director) myself, I got this answer on this subject:
So, from his point of view, it's not unreasonable to allow those templates to be applied as a house rule, but since the books came on different times, they simply couldn't replace what was written on the core rulebook to allow you to summon creatures with the entropic or resolute templates.