Yeah, every race has a distinct trophy kill if you manage to sneak up on an enemy from behind, not sure about marines though.
Predator: Literal trophy kill, wristblade in the neck, removes Marine's head with most of their spine still attached and keeps it as a trophy.
Against aliens I believe it's just a wristblade under the chin and through the top of the head.
Alien: Creepy one with Predator, I had this one done to me when I was running for the Smart Disc. Alien appears behind you and grips your shoulders while its head pops round and looks you square in the eye, you look down briefly and all you see is a tail sticking straight through your stomach.
The other one is where it sneaks up on you, turns you round and sticks its tongue through your face.