Myth One: Is it really contactless? 
Contactless payments are marketed by MasterCard as "Tap and go". If you tap, that's a contact... To differentiate itself, I guess, Visa is using "Wave" instead of "tap". Have you ever seen anyone waiving their contactless card (or a phone) when paying? Technically, if you were to wave, that could break the communication session and you would have to start all over again. Amex got it right: "hold your card close to a reader for a moment or two". Well done!

Myth Two: NFC vs contactless
The terms "contactless" and "NFC" are often freely (and wrongly) substituted. Both refer to wireless communication based on RFID. Yet, NFC technology relates primarily to mobile phones and similar devices. "Contactless" relates primarily to cards and other form factors. Also, "contactless" refers to a payment method, including EMV-compliant ones. By contrast, NFC has got nothing to do with EMV as such - an important point for understanding payments.

Myth Three: Mobile vs contactless
Just like NFC, the term "mobile" is often used in conjunction with "contactless". When a mobile phone is used for contactless payments, that involves NFC or some other "proximity" method (e.g. Bluetooth, barcode, etc). In most cases, there is also a terminal or another mobile phone involved. True "mobile" payment is done using a mobile phone alone, to send payment-related data via GSM or the Internet, i.e. you do not need to tap, wave or hold anything. Think M-Pesa.

On a humorous note, the earliest "contactless" payment dates back to 1926.

On a (serious) practical note, NFC-enabled phone - or, another device - can emulate "contactless EMV" payment without being EMV-compliant. That's where the next big disruption will come from (on both sides of payment transactions...) - when some players solve the secure element conundrum.