RFID isn't smart; it's just a little chip that harvests energy from being illuminated by a radio wave signal from the terminal, and reflects back a code. (Well, that's a passive tag; there are self-powered ones also.)
Smart cards contain a considerable embedded system for transactional processing; it's quite different from just transmitting an ID.
Correct; an RFID tag cannot hold a cryptographic secret and perform a calculation with it to prove that it knows the secret, without revealing the secret. It has no compute capability. It's just a kind of reflective beacon.
RFID: Radio Frequency Identification: passive powered by RF, returns data when powered.
NFC: Near Field Communications, is a protocol for communications, built on RFID, includes polling for readers and protocols for defined crypto and data storage/retrieval.
EMV: Eurocard/Mastercard/Visa standard for the data and crypto operations for an EMV chip, extended from physical by the use of NFC for contactless payments, primarily by replicating the data on the magstripe and adding some additional crypto and dynamic elements.
EMV is one standard for how to use an NFC card, there are others, primarily used for transit.
Smart cards contain a considerable embedded system for transactional processing; it's quite different from just transmitting an ID.