I recently saw an offer to "Buy Bitcoin Core with your credit card". Is this "Bitcoin Core" the same thing as BTC?
Kind of. People who call Bitcoin "Bitcoin Core" are referring to Bitcoin. They will also use the name "Bitcoin Legacy". but calling Bitcoin "Bitcoin Core" or "Bitcoin Legacy" is misleading.
Bitcoin Core is the reference client for Bitcoin. But it is wrong and misleading to call a coin by the name of its reference client. For example, we don't call Bitcoin Cash "Bitcoin ABC" even though its reference client is Bitcoin ABC. Nor do we call Ethererum "geth" even though its reference client is Geth.
No, Bitcoin is the token (BTC/XBT), Bitcoin Core is the software used to validate transactions. Calling Bitcoin "Bitcoin core" or "Bitcoin legacy" was a publicity stunt by Roger Ver and Bitcoin Cash to confuse people into thinking Bitcoin cash was Bitcoin, but in reality it was just a fork of the Bitcoin blockchain.
Bitcoin Core is what people download on their home computers to run a full node, don’t know exactly what that means but it includes every block of the blockchain. You can create ( or sign or whatever) your own transactions. Well, not me but most everyone else here I’m sure. BTC is Bitcoin that holds value. It is a token like BCH is Bitcoin Cash
That’s as basic as it gets