If you literally copy Bitcoin's code, you just have a Bitcoin wallet. If you start changing the code and your rules are not compatible with Bitcoin network, you will have either a hard fork or a soft fork. A soft fork means that some transactions that were valid in previous versions are invalid in new version. A hard fork is introductions of new rules that are not compatible in any way with old rules. A hard fork always results in chain split, while soft forks not always lead to chain split.

But even if you do a soft fork on with a minority chain, you will likely have a chain split. So you will have an altcoin split off Bitcoin with only your node running it. And in case of forks devs must implement replay protection and new address formats to prevent their users from suffering losses.

Copypasting Bitcoin code is not as easy as it may seem, and even if it's done more or less correctly, such coin is not getting any popularity. So most altcoin creators either make Ethereum tokens or create a new codebase for their coin, even if they heavily borrow the design from some other coin.