Is is summoned from it's home plane? It just disappears and reforms in their home plane within 24 hours, perfectly fine. No biggy.
Was it called from it's home plane? It's dead. Gone. Forever.
What does get left behind is a corpse.
And yes, devils most certainly can travel to the Material and other planes of their own accord, though that is for a rare few and usually outsiders have to rely upon creatures in the material to bring them to the plane.
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Summoned is via summon monster spells. It's not the real creature, more akin to the essence or energy of the creature. It reforms in its home plane, as noted.
Calling is the act of bringing an actual outsider here. Usually via planar binding. The outsider you call is real and not under your control (though you can create a semblance of control with magic circle against evil, dimensional anchor, and other smart contingencies.
You can get this creature to help you, but you should be particularly careful with devils (don't make an agreement, unless you're sure of it and even then). It'll cost you a good bit depending on HD. But a called creature is real and will die if you stick them with the pointy end enough times.
Calling: 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.
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.
When the spell that summoned a creature ends and the creature disappears, all the spells it has cast expire. A summoned creature cannot use any innate summoning abilities it may have.