Your garage radio gets better reception (keyword here reception) because it is a receiever (keyword here receiver) only. When you make contact with the antenna in this particular application your body becomes a bigger antenna for the radio.
As for your car transmitter it has the same effect. You are effectively increasing the size of the antenna with your body acting as a pseudo antenna.
Both applications above are PASSIVE half-duplex (one way single communication) examples. They do not apply to the sophisticated design of an ACTIVE full-duplex antenna, which is a very high speed switching (800MHz -1900MHz) transceiver that is acting as a transmitter and receiver at the same time. Which is very sensitive to impedance fluctuations.
Half duplex does not mean one way communication. It means one way at a time switching back and forth for xmit and receive. Simplex means one way communication. Your definition of full Duplex is correct.