I believe the push button start uses the same technology as the earlier “immobilizer” systems. These used a PASSIVE (no battery) Radio Frequency IDentification (RFID) system. In most of these, there is an RFID transponder device molded into the plastic part of the key (or fob). The car has an antenna that emits a radio signal that powers and wakes up the RFID transponder in the key. The key then transmits a security code back to the car. These communications use encryption. Typically the range of these systems is very short because no battery is involved. The frequency of the radio field does not change, but because of encryption, the message to allow the car to start will change.
The remote door-unlocking uses a different ACTIVE RFID system that uses a battery in the fob or key. It has a mach larger range so you can unlock the car from a distance. Of course encryption is used to prevent thieves from unlocking the car.
Infrared technology is not used in automotive applications. That is what makes your TV remote work. That is why you need to aim the remote at the TV so the IR light gets received by the TV. This technology would not work in bright daylight since sunlight is rich in IR. The sunlight would swamp-out the signal from the remote.