Oh yes. I knew there must be some difference.
Although I'm curious why it has to be a slashing rapier. Zombies?
Zombies, ghostwalkers, constructs, and anything else the DM can throw at me that's immune to piercing. He's been going it since the beginning with my arrows which are thankfully force now. Can't exactly do that with a sword.
The thinblades are all exotic, and while they do more damage, they're still piercing.
Also, it's gotta be good for Weapon Finesse. I'll check on that whip though.
EDIT: That weapon in the DMG on page 145 isn't a chain whip at all. It's a sickle attacked to chain.