The first generation of blockchains stems from the Bitcoin blockchain, the ledger underpinning the decentralized, peer-to-peer cryptocurrency that has gone from Slashdot miscellanea to a mainstream topic.
This blockchain is a distributed ledger that keeps track of all users' transactions to prevent them from double-spending their coins (a task historically entrusted to third parties: banks). To prevent attackers from gaming the system, the ledger is replicated to every computer participating in the Bitcoin network and can be updated by only one computer in the network at a time. To decide which computer earns the right to update the ledger, the system organizes every 10 minutes a race between the computers, which costs them (a lot of) energy to enter. The winner wins the right to commit the last 10 minutes of transactions to the ledger (the "block" in blockchain) and some Bitcoin as a reward for their efforts. This setup is called a proof of workconsensus mechanism.
This is where it gets interesting. Bitcoin was released as an open source projectin January 2009. In 2010, realizing that quite a few of these elements can be tweaked, the community that had aggregated around Bitcoin, often on the bitcointalk forums, started experimenting with them.
First, seeing that the Bitcoin blockchain is a form of a distributed database, the Namecoin project emerged, suggesting to store arbitrary data in its transaction database. If the blockchain can record the transfer of money, it could also record the transfer of other assets, such as domain names. This is exactly Namecoin's main use case, which went live in April 2011, two years after Bitcoin's introduction.
Where Namecoin tweaked the content of the blockchain, Litecointweaked two technical aspects: reducing the time between two blocks from 10 to 2.5 minutes and changing how the race is run (replacing the SHA-256 secure hashing algorithm with scrypt). This was possible because Bitcoin was released as open source software and Litecoin is essentially identical to Bitcoin in all other places. Litecoin was the first fork to modify the consensus mechanism, paving the way for many more.
Along the way, many more variations of the Bitcoin codebase have appeared. Some started as proposed extensions to Bitcoin, such as the Zerocash protocol, which aimed to provide transaction anonymity and fungibility but was eventually spun off into its own currency, Zcash.
While Zcash has brought its own innovations, using recent cryptographic advances known as zero-knowledge proofs, it maintains compatibility with the vast majority of the Bitcoin code base, meaning it too can benefit from upstream Bitcoin innovations.
Another project, CryptoNote, didn't use the same code base but sprouted from the same community, building on (and against) Bitcoin and again, on older ideas. Published in December 2012, it led to the creation of several cryptocurrencies, of which Monero (2014) is the best-known. Monero takes a different approach to Zcash but aims to solve the same issues: privacy and fungibility.
As is often the case in the open source world, there is more than one tool for the job.