What's the difference between ETC and ETH?

The fork discussed in this article is different from the 2017 Metropolis hard fork upgrades. The Q3 2017 Metropolis hard forks are upgrades that the whole ETH community is behind, so no forked coins are split off in their wake. See here for more details.

Much like Bitcoin and Bitcoin Cash, 'Ethereum' (ETH) and 'Ethereum Classic' (ETC) are two entirely separate currencies, despite sharing a common origin. ETH and ETC forked from each other in July 2016.

At present, Ethereum (ETH) is the much more widely accepted and used chain. To understand why, let's look at the context of the ETH - ETC split. This article will not into depth on the historical background, but to make a long story short:

There was a smart contract running on the Ethereum blockchain called the DAO (Distributed Autonomous Organization) used as a venture-capital fund for crypto-related projects. This contract had millions of ETH held in it, and due to a bug in the contract's code, there existed an exploit which a hacker used to drain the ETH balance of the smart contract. He stole hundreds of millions of dollars' worth of ETH in seconds!

https://www.cryptocompare.com/coins/guides/the-dao-the-hack-the-soft-fork-and-the-hard-fork/

The Ethereum community was in uproar. The developers and community came together and decided that the best course of action was to enact a fork that reverted this enormous theft. This forked chain is what became Ethereum (ETH) and the old chain, where the hack was never reversed, is Ethereum Classic (ETC). 

Most of the Ethereum community and developers migrated to the new chain, which is where most development now takes place. This also explains the higher market valuation on ETH compared to ETC.