Keyfobs that do a handshake are actually quite common, see the HiTag2 key transponder specifics for how its handshake works.
Even without a handshake, the code can still identify the key if it is long enough, and cars can be programmed to accept multiple keys, but almost certainly there is a handshake involved.
I believe your key probably uses a Ford type transponder chip, probably transmitting at 315MHz for long range commands like door unlock, and a lower freq for engine start (123-134KHz). For engine start, the car tells the key it wants to start and adds a challenge code, then sends to the key. The key encrypts the challenge, resulting in an 80-bit code, then truncates to 40-bits and transits back with its serial number and a checksum. The car then verifies the code, and starts if it is correct.
I am not sure if the high frequency commands use the same cipher, but they are a 1-way transmission. Similar to how a garage door opener can use 2 remotes, the car can use 2 keys to unlock doors without a handshake, as internally the car will see that the code matches a programmed key.