I always thought the blockchain operated within the ethereum network. I'm still learning a lot of this stuff. However, since Bitcoin was created first I'm assuming it has its own blockchain or ethereum and all Dapps operate within it or their own. I'm a bit confused.
No no, Ethereum and Bitcoin operate on different Blokchains. Every cryptocurrency has its own blockchain which is a record off all the transactions that ever took place. Many tokens are based on the Ethereum network called erc20 tokens.
Think of it in this way, imagine you want to send en email to someone, over yahoo for example but in order to send that email you would need to download its blockchain (record of all the emails that have been sent up until that day). Tomorrow you are sending an email but this time over hotmail, therefore you cant use the yahoo records - you would need to download the one hotmail provided.