I seemed to have gotten the wires in my head crossed. The question was intended to query what the rules for throwing the projectile caught with Snatch Arrows back is.
Is it a improvised throwing or the same deal? I.E. is a snatched arrow a d8 normal arrow, or improvised?
An arrow (or other piece of ammunition) would be treated as an improvised weapon if thrown. A thrown weapon that is snatched is treated as a thrown weapon when thrown back.
Note that only thrown weapons can be "immediately thrown back" with the Snatch Arrows feat. Projectiles, once caught, can be used as an improvised weapon on the character's turn.