This is a question that I see commonly asked, and these are two totally different things. This article will give an overview of the two things, which should hopefully answer the question in the title.
Overview of Zwift Power
Zwift Power is a website that Zwift acquired back in 2020. Zwift Power takes in the results from Zwift races, and based on event organisers settings, removes riders who are not following the ‘rules’ that the organisers set. This could be removing riders on Zpower(ZP for short), sandbaggers(riders who aren’t racing in their proper category), cheaters(incorrect power). Sign up for Zwift Power here: https://zwiftpower.com/events.php.
Overview of ZPower
ZPower is what many beginner Zwifters start out riding on. When you are Zwifting without a power source, just a speed and cadence sensor, Zwift is actually estimating your power output. These riders often get flagged or disqualified on the Zwift Power results. Zpower can be accurate in some situations, but in many it is not because of a dumb trainer that isn’t compatible, wrong settings, etc.