What are the basic differences between MMC and eMMC storage?
In short, there is no fundamental difference. Modern MMC is eMMC molded into plasic case. Or eMMC is a naked BGA chip soldered on-board. "e" simply means "embedded". Support for optional modes changes with revision of specifications, 1.0, 2.0, 3.x, 4.x, now at 5.2, with ever increasing transfer speeds.
In older days the MMC plastic was made of two chips inside, MMC interface controller, and a parallel flash. Today the controller (MMC-to-flash) is integrated into single chip.
Where can I find examples code and/or the communication protocol to
access eMMC memory?
Regarding the communication protocol, MMC is an open standard. But you don't need to study the low-level bus protocol, since the application will be accessing the interface via MMC/SD host controller inside the SoC/MCU. You will still likely need to follow all discovery protocols in accord with corresponding sequencing/initialization. Typical controller architecture (register access etc.) can be found in this stand-alone chip example SDIO101A from NXP. MCU provider will likely supply examples of driver.