Most keyless start systems have a backup physical key[1] hidden inside the remote fob and will use very short range RFID [2] similar to older physical turn keys and their immobiliser chips to authenticate with the car ECU and allow the engine to start.
I'm aware of this as I have owned cars with this feature. Modern cars do not use the physical key to "start". It's mostly only to open the driver side door.
See: https://www.youtube.com/watch?v=BttKQ6K-Y74
RFID/NFC is used to actually start the car like you pointed out.
On all current Tesla cars, they fobs and keycards can both unlock and start the car, making a physical key pointless.