Apps that allow you to manage your cryptocurrency funds are called wallets. All wallets receive an address and a seed phrase (private key) upon creation. Wallets use the address to send and receive funds on blockchain networks. Provided seed phrases are provided as a security measure to protect the wallet. Almost every wallet can fall into one of two categories, hot wallets or cold wallets.
Wallet Apps that are based entirely online are called hot wallets. Hot wallets are more susceptible to hacks than cold wallets. There are two types of hot wallets, custodial and non-custodial. Popular hot wallets include Metamask and Trustwallet – these are both popular among yield farmers.
Some wallet apps will manage seed phrases internally and offer security solutions to protect said seed phrases; managed seed phrase wallets are called custodial wallets. Most commonly, exchanges offer custodial wallets. Custodial wallet providers usually do not provide users with the seed phrase to the managed wallet(s).
Non-custodial wallets will provide the user with the seed phrase upon wallet creation; it is up to the user to protect that information.
Cold Wallets are offline wallets; they are hardware with an internal app that stores keys and offers more protections. Cold wallets are almost all non-custodial.
It is standard practice to write and store your key offline and never share your key with anyone.