There is bitcoin core wallet..which you download on your computer and you have 100% full ownership of your bitcoin BUT etheruem NEVER has anything like this..most of the wallets are either on a website or some company or some service
What happens if these websites, companies and services go burst(i mean history shows this, dont be in denial please)
Please answer below
What is an Ethereum wallet, and which one should I use?
Wallets are applications that make it easy to hold and send ETH, as well as
interact with applications built on Ethereum.
Want to install a wallet? Here are a few options:
MetaMask: browser extension and mobile wallet for iOS and Android
MyCrypto: web-based wallet
TrustWallet: mobile wallet for iOS and Android
MyEtherWallet: client-side wallet
Argent: mobile wallet for iOS and Android, optimized for DeFi
Coinbase Wallet: mobile wallet for iOS and Android
Gnosis Safe: security oriented multi-signature wallet