Conjuration (Calling) spells physically take a creature from another plane and move them to you. If killed, they stay dead. A calling spell grants the creature a one time ability to return home, but can limit circumstanced under which they may use that ability.
Conjuration (Summoning) spells brings a creature to a place you designate, not necessarily from another plane. If killed, dispelled, or the duration elapses, the creature is sent back. If dropped to 0hp or killed the creature is sent back, but reforms after 24 hours, during which it cannot be summoned again.
Mount is a Conjuration (Summoning) spell.
If it were a (Calling) spell, you'd actually take a horse from somewhere else, bring it to you. It'd be a real, physical horse, that was probably hapily munching hay somewhere or sleeping or whatnot, up until the point where you made it be where you are. If you cut it, it bleeds. If you kill it, it dies. You conjure up A Horse.
If it were a (Summoning) spell, which it is, you cast the spell and a horse appears to serve you. It wasn't doing anything before you conjured it, it probably has nothing in it's life other than being summoned and having people ride it. If you cut it, it bleeds. If you kill it, it goes away, doesn't die, and is just fine and dandy a day later. You conjure up Horse
The Mount spell basically takes magic and makes it be a horse for the duration of the spell.