Every wallet in the Ethereum ecosystem consists of two parts - public key and private key. Trust Wallet stores your private key directly on your device. There are a couple of formats Trust can display your private key in -
- Keystore JSON is your private key, encrypted with a password for better protection.
- Private key - an unencrypted collection of numbers and letters that unlocks access to your address on various blockchains
- Mnemonic phrase - 12 words used to secure your private key. Much easier to remember.
No service should ever ask you for your private key (or Keystore with the password). Anyone with your private key can access your wallet and have FULL CONTROL of your funds.