Best guess is you have a big switch near the radio marked something like PARK / TRAVEL. (Click the picture below to make larger.)
That switch controls if the radio is on all the time....
Park is on without the key.... Like you are in your camp spot but want to turn on the radio without turning the ignition key.
Travel functions with the ignition on and off when you turn the key for the engine.
We dont know what kind of radio you have as you didn't tell us or provide a picture, but I have NEVER seen a radio anywhere that didn't have its own power button to turn it fully off and on... So beside the switch there is still probably a power on/off with the radio itself.
Hope this helps.
2019 Fleetwood Southwind 37 F
2018 Jeep Wrangler JL - towing
2020 Jeep Gladiator not towing
We RV'd ALL of the lower 48 states and into Canada