Bitcoin Core is the reference implementation for the Bitcoin source code, meaning all other implementations look to Bitcoin Core for guidance on maintaining consensus and upgrading. This is where most users go to download the source code.
Bitcoin Core provides software for both a node and a wallet, although most users prefer to use Bitcoin Core for its node and use third party software for their wallet. There are alternatives to Bitcoin Core’s node software, but Core is the dominant implementation. Anyone wishing to download Bitcoin’s software and run a node can access Bitcoin Core via their website or their GitHub page.
Bitcoin Core was created by Satoshi Nakamoto, and although ownership has been passed down and many upgrades have been added to the project, the latest version and Satoshi’s original version are still compatible.
Bitcoin Core is an open source project. This means that anyone can copy the source code and edit it as they see fit. If a developer wants to improve Bitcoin, they can publish the changes they have made and propose that their changes be included in Bitcoin Core. Many developers choose to contribute to Bitcoin Core through code, review, and discussion. However, there is no authoritative entity that pays developers to work for Bitcoin Core. Instead, Bitcoin companies and individuals partially fund these developers through donations and grants.