Trying to catch up with the news, so please bear with me.
Do I understand it correctly that BTC and BCH use the same address space and the same principles of building a blockchain out of transactions but they differ in how transactions are signed now, making them mutually invalid?
In the light of the above, if I decide to spend my pre-fork BTC txout into BCH, I just need to issue a BCH-signed transaction for that txout, right?
After I do that, will this txout be still unspent from BTC network point of view (since my BCH transaction is invalid in BTC and won't go into BTC blockchain)?
As far as the users of Bitcoin/Bitcoin Cash are concerned there is very little noticeable difference on the frontend when using either currency. The main difference between these coins is the fact that, given equal hashrate, BCC protocol allows for more transactions per second which translates to faster payments and lower fees.
Bitcoin is being forked into two different currencies, each sharing a common transaction history from before the fork. Bitcoin Cash is the chain supported by the miners who wanted larger blocks, and the regular Bitcoin chain is the one supported by the core developers. On the day of the fork, every BTC address suddenly had a twin existing on the BCH network. If, at the time of the fork, an address had 0.45 Bitcoin, then its twin on the BCH network had 0.45 Bitcoin Cash after the fork.