It's literally a split. A fork of the code and the blockchain. If you used a wallet that supports Bitcoin Cash before the split, like Bitcoin ABC or Bitcoin Unlimited, and you hate money, you could ignore Bitcoin Core and go on as if nothing happened. Nothing was distributed. Existing private keys and addresses are simply valid on two blockchains now.
Bitcoin Cash was 'distributed' on exchanges (and Bitfinex users only received 0.85 BCH per BTC), but money on exchanges is fake anyway - just balances in a company's ledger that you hope will be credited as real money when you withdraw.
Now you could argue that Bitcoin Cash is not legit Bitcoin because it wasn't approved by the Bitcoin Core developers. And that exchanges should ignore it because anyone could create a split. But Bitcoin Core supporters don't like to appeal to authority, so they're using all kinds of fallacies and underhanded tactics instead. Like calling it Bcash, creating a totally different logo, having a supposed big-block supporter say he lost faith in Roger Ver on /r/btc because the price went down, and pointing out any transitional problems. They laugh at the slow blocks, while they would have called a faster difficulty adjustment unsafe. The trolls don't seem to realize that they're only drawing attention to Bitcoin Cash.