When you set up or select a "model", its only storing the settings that you have set. Its not like changing channels on the TV...in other words, when you select a different model, it's not like you are "changing the channel" to select a different receiver (the Futaba FHSS/S-FHSS is a slight exception). If you had 10 cars, 10 receivers and 10 models programmed into your radio (and if all the receivers have been properly bound), all 10 would do something with throttle and steering commands.

It appears that your system is functioning just fine