Are the Boeing MCAS and Airbus Alpha Protection systems the same?
No, the two systems are completely different.

The MCAS of the new Boeing 737 MAX was introduced to help the pilots lower the nose in high angle of attack situations by applying down stabilator trim. This was necessary because the engines are mounted further forwards compared to the previous NG models.

Note: We do not know whether or not MCAS caused the recent crash in Ethiopia yet, it is a bit premature to jump to conclusions now!

The Alpha Protection on Airbus aircraft is part of the fly-by-wire control (What is the Alpha protection?) and will limit control inputs from the pilots instead of applying trim. This is very different from how MCAS works.