Good catch. I haven't thoroughly read the OP, but from the little bit I have read, it looks like they refer to the currency of Zerocash as zerocoins (the uppercase on Zerocash and lowercase on Zerocoin come from the paper), and the OP seems to be by the same authors.
Can anyone comment on how simmilar/different Zerocash is from the original Zerocoin? Did they just improve the underlying crypto, or is there a more high level change involved?
Zerocoin basically implemented a decenteralized 'mix' via a blind accumulator. Zerocash uses zero knoweldge proofs of execution for general computation so that basically all properties of a coin can be completely blinded.
In ZeroCoin, coins— all of equal denomination— go into a bag (one bag per denomination), and coins come out of the bag and you can't tell which was which (except, of course it can't come out until after it's gone in.). In Zerocash its more like everything is completely encrypted, even the values, the network knows that its all valid due to zero knoweldge proofs, but only the transaction participants know any of the details of the transactions at all.
In some ways Zerocash is really the some of the most pedestrian applications of the ZK-SNARK technology, ... prepare to have your mind blown and go read some at http://www.scipr-lab.org/
(What you describe is Zerocoin, the OP is about Zerocash)