Bitcoin Cash is an altcoin, i.e., a Bitcoin-like protocol and network derived from the hard-working Bitcoin chain state. Bitcoin Classic was first a hard work project and then an alternative implementation of the Bitcoin protocol first and then the Bitcoin Cash protocol.
Originally, Bitcoin Classic was a tough proposition that called for block block increases to be activated with 75% hashrat support. To this end, the Bitcoin Classic repository maintained only the changes necessary to implement the said block size increase, re-basing this in addition to the latest changes in the Bitcoin Core repository. When it became apparent that Classic was too poorly supported, the Classic repository began to lag behind,
data warehouse began to lag behind, the work was later terminated.
Later, the Bitcoin Classic repository was revived by a developer as an alternative implementation of the Bitcoin protocol. Several other changes have been made to this repository instead of just maintaining the block size increase code. For a while, Bitcoin Classic collaborated with Bitcoin Unlimited, e.g. both implementations provide support for thin arrays. Later, Bitcoin Classic maintained an alternative implementation of the Bitcoin Cash protocol. It has recently been completely abolished.
See Checking / Querying Address Balance in Electrum via Command Line / RPC
Bitcoin Cash is essentially a clone of the existing Bitcoin block chain, which has one important feature: additional block size capacity. Those who owned Bitcoin before the split now own the same amount of Bitcoin Cash, meaning Bitcoin Cash and Bitcoin each have 16.5 million units in circulation. Multiply the latest $ 607 price of Bitcoin Cash, 16.5 million times, to reach the $ 10.8 billion market cap, making the third most valuable cryptocurrency about 16% of Bitcoin’s $ 69 billion market value.
There is another HUGE difference - there is no platform for use or distribution of any kind - i.e. web stores that buy bitcoin do not automatically buy bitcoin cash - and the ATM network that sells bitcoins not only automatically generates bitcoin cash.