Help with a beginner question

I have had my ETH on an exchange for quite a while. I’ve transferred all of my BTC to my trezor wallet. If I do the same with my ethereum will I need to pay these high gas fees that I keep hearing about? If not, can someone explain to me under what circumstances I would pay these high fees. And if so, can someone tell me how I can monitor and wait for the fees to be historically low. Maybe gas fees are just for developers ? I just don’t know