As Bitcoin Cash is a result of a chain split from Bitcoin, it shares much of Bitcoin’s fundamental workings. In fact, they even share the same history.Due to it being a fork of bitcoin, all on-chain data prior to the split are inherited. If you owned 1 bitcoin before the creation of Bitcoin Cash, you now have 1 BTC and 1 BCH, which can be signed using the same private keys.
However, Bitcoin and Bitcoin Cash are not non-interoperable. You cannot send your Bitcoin Cash to the Bitcoin network and somehow own 2 BTC. Your bitcoin cash and bitcoin now exist on two different sets of blockchains.
One of the main differences between Bitcoin and Bitcoin Cash is the block size limit and transaction fee. As Bitcoin Cash has bigger blocks and arguably lower usage, sending Bitcoin Cash on the network is relatively cheaper and faster than if done on Bitcoin. In that sense, Bitcoin Cash does serve as a quicker and more efficient form of digital currency as extolled by Bitcoin Cash proponents.