I want to know what is different between using electrum and hosting a full node (that requires bandwith and a lot of stroage)?
The difference between running a full-node and using an SPV client like Electrum is that with your own node, you check and verify the entire history of transactions from the beginning of Bitcoin. With a full node, you are just trusting someone else and you aren't doing the verification on your end.
Electrum servers can be operated by malicious parties who can find out things about you to de-anonymize you. By connecting to them, they will know the balance of all your addresses connected to that wallet, including the unused ones. They will also know your IP address and the version of your client. With a full-node, you aren't leaking that info because you are running that server.