RFID and NFC are wireless RF technologies, which are the biggest common denominator.
RFID is a general concept of radio frequency identification, according to frequency division contains low-frequency, High-frequency (13.56MHz), UHF, microwave, and so on. Reader and writer can read and write tag data information, the role of distance depends on reader power, reader antenna gain value, label antenna size. In general, the higher values, the farther reading.
NFC frequencies are also the same. 13.56MHz, and compatible with most RFID high frequency related standards (some are not compatible), but the provision of NFC function distance can not be very far.
Now say a different point, RFID reader and tag can be a one-to-many relationship (Low-frequency and High-frequency 14443 is a pair of one).
NFC is definitely a pair of relationships. NFC can have three modes, analog cards (tags), analog card reader, point-to-point.
RFID with different band standards, data format is different. NFC standard data format is ndef format. Although NFC can also read some high-frequency tags, but still will find that some high-frequency tags can not be read, which is said to be the NFC-compatible part of the high frequency standard (which is also linked to NFC reader chip, the technical barriers between different manufacturers), this is the reason.