Moz is an SEO company, it has devised its own ranking system that tries to analyze the power of the domain and web pages based on the number of backlinks and quality of backlinks. For instance, if your website has 100 backlinks and if the website on the same niche has 50 backlinks, your website will have higher domain authority and higher page authority. Moz ranking is good to check the SEO power of your website. Search engines like Google, Yahoo, Bing have their own ranking system based on their own unique algorithm. They do not follow what ranking system other companies are using. While you can have higher domain authority and page authority of you have a lot of backlinks, getting high rank on Google is not just about having a lot of backlinks, the google rank si also based on a number of other factors like keyword usage, content quality, content originality, etc. What ultimately matters is your website's position on google search engine result page (or bing or yaahoo, for that matter), because that's how you get organic traffic. When your site receives organic traffic, you are very much likely to make money from your website because organic traffic has high conversion.