Not addresses, but transactions. Let's say you have 1 BTC at address 1Addr.... After the split, you have 1 BTC on the BTC network at address 1Addr... and 1 Bitcoin Cash on the Bitcoin Cash network, also at address 1Addr.... What this means is that if you were to have a transaction that spends 1 Bitcoin Cash to address 1Xyz..., a type of attack known as a replay attack would't be possible. A replay attack is an attack where someone copies your transaction exactly, and uses it on the other network. In this example, if the replay attack was performed (it can't because BCC has features to prevent it), then your 1 BTC on the Bitcoin network would also move to 1Xyz... (BTC address), even though you only intended to send BCC to 1Xyz...