Pathfinder-1e

• Summoned creatures are not killed when they drop to zero hit points, regardless of what plane they are on.

• Called creatures die when they are killed, regardless of what plane they are on.

Pathfinder-2e

• Creatures with the summoned trait are not killed when they drop to zero hit points, regardless of what plane they are on.

• Calling doesn't exist, but the Gate spell does, and it does not add the summoned trait to the subject of the Gate spell, so they have no special protection from being killed.

In Pathfinder-1e (as well as Dungeons and Dragons 3.5), summons are not killed when they drop to zero hit points. It does not matter whether they are on their own plane or not.

Summoning:

A summoning spell instantly brings a creature or object to a place you designate. When the spell ends or is dispelled, a summoned creature is instantly sent back to where it came from, but a summoned object is not sent back unless the spell description specifically indicates this. A summoned creature also goes away if it is killed or if its hit points drop to 0 or lower, but it is not really dead. It takes 24 hours for the creature to reform, during which time it can’t be summoned again.

Calling is different. In Pathfinder-1e, under Conjuration you find this entry for the calling subschool,

a calling spell transports a creature from another plane to the plane you are on. The spell grants the creature the one-time ability to return to its plane of origin, although the spell may limit the circumstances under which this is possible. Creatures who are called actually die when they are killed; they do not disappear and reform, as do those brought by a summoning spell (see below). The duration of a calling spell is instantaneous, which means that the called creature can’t be dispelled.

Outsiders are not afforded protection with other modes of travel besides summoning, whether by spells like Gate or Planar Ally, or by a magic portal, as these are Conjuration (Calling).

However, if they were to use a spell like Astral Projection to travel,

If the second body or the astral form is slain, the cord simply returns to your body where it rests on the Material Plane, thereby reviving it from its state of suspended animation. This is a traumatic affair, however, and you gain two permanent negative levels if your second body or astral form is slain.

Note: the italics portion is unique to Pathfinder-1e. 3.5 did not have this negative effect.

In the Fiendish Codex Volumes 1 and 2 for Dungeons and Dragons 3.5, there is mention of demons and devils not actually dying, but the consequences are severe enough, they are effectively dead.

In the Fiendish Codex I: Hordes of the Abyss, pp 9

if [a demon] is killed outside the Abyss, its “essence” falls back into the raw chaos of the Abyss, where it is then be reformed as a new demon.

And in the Fiendish Codex II: Tyrants of the Nine Hells, pp 18

A devil slain outside Baator [Hell] devolves into a puddle of foamy, stinking ooze over a period of 3 to 9 minutes [...] a slain devil returns to Baator 99 years later [...] the devil might experience no repercussions, or it might face demotion for failure

In Pathfinder-2e, type/subtype is now a trait. Nothing in the entries for demons or devils, similar to previous editions, mentions anything about an immunity to being killed on another plane. Also, Summoning is not present in the Magical Schools, but Conjuration is,

CONJURATION

Conjuration spells transport creatures via teleportation, create an object, or bring a creature or object from somewhere else (typically from another plane) to follow your commands.

Conjuration spells often have the teleportation trait, and the creatures summoned by conjuration spells have the summoned trait.

SUMMONED (TRAIT)

A creature called by a conjuration spell or effect gains the summoned trait. A summoned creature can’t summon other creatures, create things of value, or cast spells that require a cost. It has the minion trait. If it tries to cast a spell of equal or higher level than the spell that summoned it, it overpowers the summoning magic, causing the summoned creature’s spell to fail and the summon spell to end. Otherwise, the summoned creature uses the standard abilities for a creature of its kind. It generally attacks your enemies to the best of its abilities. If you can communicate with it, you can attempt to command it, but the GM determines the degree to which it follows your commands. Immediately when you finish Casting the Spell, the summoned creature uses its 2 actions for that turn. Summoned creatures can be banished by various spells and effects. They are automatically banished if reduced to 0 Hit Points or if the spell that called them ends.

In Pathfinder-1e (and DnD3.5e), summoned creatures could not be killed, but called creatures could (regardless of whether they are on their home plane).

In Pathfinder-2e, all conjured creatures gain the summoned trait, and thus cannot be killed.

In Pathfinder-1e there isn't any immunity solely based on being an outsider (save the lore in the Fiendish codexes).

However, the Gate spell still exists, and it does not mention anything about conjuration or summoning, so I assume the same would apply in Pathfinder-2e; if a creature travels through a gate to another plane, they have no protection from being killed.

While the question is in regards to Pathfinder, I should note, in Dungeons and Dragons 5th Edition, this has changed. Demons and devils can only be killed in their home plane.