Media Independent Interface (MII) vs Media Dependent Interface (MDI)
MDI is a type of Ethernet port connection using twisted pair cabling. The MDI is the component of the media attachment unit that provides the physical and electrical connection to the cabling medium which is used to connect network devices (hubs and switches) with other hubs and switches without the use of a crossover cable or null modem.

Where MII is Media Independent Interface which is responsible for the connectivity between MAC and PHY as you mentioned.