Murch

Bitcoin Core is the main software that runs the Bitcoin network, the direct descendant of Satoshi's original program. It is free and open source, maintained by volunteers and grant-funded developers.

A BIP is a public design document that proposes a change or a standard for Bitcoin. Writing a BIP does not change Bitcoin; node operators decide by running software that implements it.

A full node is a computer running Bitcoin software that checks every block and transaction against the rules by itself. With your own node you don't have to trust anyone about your balance.