But if you are using a wallet like a hardware wallet, then you could call that wallet a cold wallet or offline wallet because it will not be running all the time, whereas Trust wallet will run as long as your phone or any other device is online.
Being online or offline has nothing to do with how much you run your wallet.
A wallet is offline if your keys are generated and kept offline. Even if your hardware wallet is always connected to your computer and it's always running, your wallet is still offline. In the case you use electrum to generate a wallet on an online device, it can't be considered as a cold wallet even if you delete your wallet immediately and never use it again.