Communication protocols
My feeble attempt at definition would be that an interface is what you use to exchange information over. 

The protocol is how you interpret the information you get and how you are expected to respond. 

Wikipedia:   


Interface (computing), a point of interaction between hardware, software, or a combination of the two.
Communication protocol: a defined set of rules and regulations that determine how data is transmitted in telecommunications and computer networking 


Note that for SPI there is no interpretation (and no standardization) . It just pumps data through the interface.
This leads to problems as SPI interfaces can electrically be compatible but behave very different. 

e.g. an 12 bit DAC can work with 12 clocks cycles and be write only.
There is no way that would be able to talk to an EEPROM where you need an address, data read, data write, sector erase etc.