To properly explain the differences between Ethereum (ETH) and Ethereum Classic (ETC) an examination into the history of this blockchain is necessary. And the story begins in 2016 with a hack to a third party application (The DAO) on the Ethereum chain wherein approximately 3.6 million Ethereum was stolen (at the time worth approximately $50 Million). At the time, this amount was not insignificant as it comprised about 5% of the total of Ethereum then in circulation.
The developers of Ethereum at the time decided that an erasure of the hack was in order and that the money stolen should be added back to the accounts of the original owners. To accomplish this a hard fork of the chain was initiated. The resulting new ledger created (the one reversing the hack and restoring the accounts) became what we now know as the 'Main Ethereum Blockchain' (ETH) while the original unchanged version of the ledger (containing the hack) was renamed to what we now know as Ethereum Classic (ETC).
While this hard fork of Ethereum may seem confusing, it is not so if the divide is viewed in terms of the philosophy serving as the basis behind each of the choices:
(ETH) - do you accept a revised distributed ledger in a blockchain that was altered to remove a successful hack from its record.
(ETC): do you prefer an unchanged (immutable) ledger containing the entire history of the chain, including the successful hack.
The ETH chain to this day remains the more popular choice of the two. The majority of users, especially those who lost coins in the hack, chose the ETH chain. In addition, the ETH chain is supported by one Vitalik Buterin, the project's main creator, whose reputation and influence is widely accepted by the cryptocurrency community.
However, the foregoing does not negate the fact that the ETC community possesses support as well, just to a lesser degree. It is these ETC supporters who adhere to the original ledger as it contains the true unchanged history of the chain. It is the ETC supporters belief that this hard fork decried the "code is king" spirit and prevention of subjective human manipulation climate for which was the purpose of developing blockchain technology in the first place. Their position is firm, in contrast to ETH, that immutable transactions are an incontrovertible basis of the blockchain which sets the blockchain apart from the manipulations present in traditional financial structures. It is the clear tenet of the ETC proponents that an immutable ledger should not be compromised, even for the best of intentions.
Turning now to the structural elements of the ETH chain and the ETC chain, the two are not dissimilar at all as the ETC chain is essentially a clone of the ETH chain. Both systems are purposed to be smart contract platforms upon which decentralized applications may be built, so the functionality aspects of both are identical. In fact, the chains are truly identical up to block 1,920,000 when the hack originally occurred and it was at this block the two systems diverged. From block 1,920,000 forward, any update to the protocol of one of the chains is no longer present in the other chain with the reverse being held true as well.
With the coming transformation of the ETH system from a Proof-of-Work to a Proof-of-Stake consensus mechanism, more commonly referred to as "ETH 2.0", a major upgrade will occur in the ETH protocol, but the same will be unreflected in the ETC protocol. As such, a further significant divergence in the structural functionality of the two systems will be experienced.
As time has passed since the original hard fork, it has become apparent that the ETC chain may be relaxing it's strict interpretations policies seeking greater interoperability with the ETH chain (and other chains). The ETC community experienced two major upgrades on this front - in 2019, Atlantis and in 2020, Agharta. Going forward only time will tell if the various splits and forks in the overall Ethereum ecosystem will permit both ETH and ETC to achieve a degree of interoperability while independently furthering development within their own separate communities according to the will of its system's members.