Do NPs and Command Cards do the same damage every time?

No, outside buffs and bonuses from card order (exept NP card), damage also gets multiplied by random value between 0.9 and 1.1

It does between a certain range each time. Here’s a link for a damage calculator
https://www.google.com/amp/s/amp.reddit.com/r/grandorder/comments/6xnmh2/updated_fgo_npdamagestar_calculator/