Zcoin is NOT a fork of Zcash in anyway.
First of all Zerocoin is the tech, Zcoin is the coin, similarly to how Zerocash is the tech and, Zcash the coin.
Zcoin uses Zerocoin technology from the Zerocoin paper.
http://spar.isi.jhu.edu/~mgreen/ZerocoinOakland.pdfThis is a very well peer reviewed paper.
Zcash uses Zerocash.
http://zerocash-project.org/media/pdf/zerocash-extended-20140518.pdfAlthough Zerocash is a development from Zerocoin meant to address certain perceived shortcomings of Zerocoin, they are not simple forks of each other and rely on different protocols.
Zerocash was meant to improve on Zerocoin on these issues:
a) Zerocoin still requires a basecoin to convert back before being allowed to spend. Zerocash has no more basecoin
b) Zerocash's proofs are much more efficient and smaller than Zerocoin's
c) Zerocoin uses fixed denominations to mint (1, 25, 50, 100) while Zerocash is not subject to such limitations
d) Greater anonymity with Zerocash since sender/receiver/amount are all obscured.
However Zerocoin's advantage over Zerocash are as follows:
a) While still retaining the basecoin and a lot of the Bitcoin core code, it is a lot easier to integrate to existing Bitcoin merchants/etc.
b) Although Zerocoin's proofs are larger and occupies more storage space, the computational requirements to generate a private transaction are many times faster. Zcash requires large amounts of RAM and minutes of computational time. Zerocoin requires seconds to use and is not memory intensive. Basically Zerocoin uses more storage space but is computationally much less intensive.
c) Parameter generation for both Zcoin and Zcash requires a trusted setup but Zcoin's parameters are arguably less controversial. (
https://github.com/zcoinofficial/zcoin/wiki/Parameters-in-set-up-phase-for-Zerocoin-in-ZCoin)
d) Most importantly is that in Zcoin, total supply is still visible so if there's a flaw and someone is secretly creating coins for themselves, this can be much more easily detected. With Zcash, because everything is hidden, if a flaw is exploited, it may be almost impossible to detect!
e) Zerocoin's tech is more peer reviewed and better understood than Zcash's. Zcash's use of zero knowledge proofs uses ZK-Snarks which very few people understand. Even Zooko himself admits he doesn't understand it (
https://www.youtube.com/watch?v=P6RLjcGVUnw&feature=youtu.be&t=17m30s). Note that Zerocoin's paper was only like 15 pages. Zcash's paper is more than 50 pages so Zcash's is considerably more complex which means more things that can go wrong. This is why Zcash had to spend so much money on multiple security companies auditing on its critical components and bugs (including some serious ones have been found). A security audit is also not fool proof as the DAO exposed and which is why Zcash also uses multiple companies to audit.
Zcash is pretty neat technology and I think is a very amazing innovation but I do think that Zerocoin has a role to play. Its anonymity is still amazingly good with a much larger traceability set than previous anonymity implementations (basically all the previous Zcoins minted), it can be much more readily used today with existing vendors/merchants and can be used in a wide variety of devices today.
Calling Zcoin a 'Zcash fork' is ignorant and shows a lack of understanding behind the large amount of work put into both these projects.
