Bitcoin Core is programmed to decide which block chain contains valid transactions. The users of Bitcoin Core only accept transactions for that block chain, making it, according to its supporters, the Bitcoin block chain others want to use.
Bitcoin Core is the canonical way to run Bitcoin. If you want to send or receive Bitcoin or understand how it works, installing and running Bitcoin Core is a must. If you are not a technical user, you may use Umbrel as a wrapper to Bitcoin Core, which will install it and manage it for you.
Electrum needs a Bitcoin Node to run. You can run your own Bitcoin Core service and connect it to Electrum for a full stack, self-custodial Bitcoin wallet. You may run a public Bitcoin Core node, so other people with Electrum use it to verify their transactions, helping the network work faster.
