There are literally dozens of bitcoin core alts right now out there but it is very hard to weed out the definition of what an alt is
Nope. There are various Bitcoin forks. But Bitcoin Core is just a Bitcoin client. There is no currency called Bitcoin Core, so there is no fork of it.
https://en.bitcoin.it/wiki/ClientsA bitcoin client is the end-user software that facilitates private key generation and security, payment sending on behalf of a private key.