The iPhone does not currently allow access to the NFC hardware by any 3rd party app. It's unclear if or when this will change. Apple's own iPhone registers in the Apple store use a custom case to read Apple Pay, instead of using the built in NFC hardware.

NFC is a subset of RFID. Specifically it passive and uses the 13.26 MHz frequency that passive RFID can use. Passive RFID has two other frequencies that it may use. RFID was intended for longer range scanning, while NFC is intended for contact or very close scanning.

Your ID card may be NFC, or RFID using 13.26 MHz.