Not even close to the same.
Mummies, are like unholy protectors. Yes they rise from the dead, but they only do so to protect their resting grounds. After fulfilling this purpose, they go back to 'sleep' untill once again needed. They also possess the ability to curse those whom disturb their resting places. And, if a mummy bites you, you don't turn into a mummy.
Zombies don't protect anything. They rise from the dead for the sole purpose of feeding, and turning others. And the only way to put a zombie to rest is to destroy their brain.