For the most part, Ethereum Classic is identical to Ethereum. ETC was the result of disputes arising from a hack of DAO, a smart contract that would work as a venture fund, where everyone that contributed to the fund would get to vote on what projects/proposals get funded. The DAO became the biggest crowd fund ever, with $240,000,000 in value, all stored in ETH inside the contract. An exploit was found in the contract and used to acquire 3 million ETH from the contract. This led to a loss of $40,000,000 from the contract. Following the breach, it was decided that there would be a hard fork was made in the system which split the Ethereum network between those who wanted to restore the funds (ETH) and those who valued immutability over returning of funds (ETC).
If you look at things technically, the loss was not really a hack but rather an exploitation of a vulnerability in the system. The main Ethereum community wanted to carry out a hard fork so that investors would be able to get their money back and so that the people behind the exploit would lose their money. While most developers agreed with the idea of returning funds to investors, a minority strongly opposed the idea as they believed that code should be law and that the principles of immutability should not be compromised. They wanted to continue operations on the old blockchain rather than creating a new one. In principle, if an event occurs on the blockchain, it should not be reversed.
The two blockchains are identical in many ways but differ in ideology. Major differences can be spotted from the period of the hardfork. There are several updates that the ETH team have made which the ETC have chosen not to make. For example, while the ETH team looks to switch to a proof of stake consensus mechanism, the ETC community did not plan to follow suit. While the majority of miners and developers are on the ETH blockchain, the ETC community is markedly smaller but still driven by passion for a decentralised future.
Many would say collaboration between both camps has improved over time. This is an important step for both communities as they continue to share more partners in the space. Synergies can be achieved with deeper relationships formed between the two communities. They both continue to enjoy relatively high interest from investors and community builders alike.