There are a few conflated terms here 
The P71 chip from NXP that the Apex Flex is built with has a hardware version that can do Mifare Classic card emulation, but that feature is not included in the version of P71 used for the Apex Flex.
The Mifare Classic chip type (S50) is not actually NFC compliant. The term NFC means a specific type of RFID transponder that conforms to the NFC Forum standard for NFC Types 1 through 5, and the Mifare Classic does not, therefore it is not an NFC compliant RFID transponder like the NTAG216 or other types of “NFC chips”.
The NFC Sharing application for Apex Flex means you can share data using a standard NFC defined NDEF container (an NDEF “message” that contains one or more NDEF “records” with payloads). This can be used for many things, including just sharing text etc.