Does an attack that is "deflected" count as a miss?
It depends on the ability that is deflecting the attack.
For example, the Deflect Arrows feat says, "Once per round when you would normally be hit with an attack from a ranged weapon, you may deflect it so that you take no damage from it." It doesn't say the attack is a miss or is treated as a miss—instead, you take no damage from the attack. Because it is not a miss, effects that would trigger on a miss (such as Efreeti Style or Snake Fang) are not triggered.
Likewise, the Crane Wing feat uses similar language and does not say the deflected attack is a miss or treated as a miss.
Note that the Snatch Arrows feat counts as a deflected attack—you do not take damage if you choose to catch the weapons instead of just deflecting it, and catching the weapon does not mean the attack was a miss.
Update: If the attack is deflected, not only does the target take no damage, but any other effects (ability drain, negative levels, harmful conditions, and so on) associated with that attack do not occur. If the deflected attack is a touch spell or other effect that requires "holding the charge," the charge is not expended. For example, if a ghoul's claw attack is deflected, the target is not subject to the ghoul's paralysis ability from the attack. If a shocking grasp touch attack is deflected, the attacker is still "holding the charge."
How does Deflect Arrows work with Manyshot?
Deflect Arrows works only once per round. Manyshot allows an archer to shoot multiple arrows, but you only make one attack roll, so Deflect Arrows would block all arrows grouped in anyone particular Manyshot attack.