ShareIt or Xender (both on play store). They use Wifi direct to transfer files. ShareIt is cross platform and can transfer between phone and pc as well. Not sure about Xender.
HotKnot is available on many Chinese phones. It's a type of, but not compatible with, NFC. It's a bit slow though, but cheaper to manufacture and doesn't require any pairing to use.
When the two screens are near each other, their physics are used in such a way that allows one of them to act as a transmitter and the other one as a receiver.
Telegram is also an option.