Domain authority is a measure of the power of a domain name and is one of many search engine ranking factors. Domain authority is based on three factors: Age, Popularity, and Size. SEO gurus Moz can be credited with the metric known as DA or domain authority.
Page Authority is a score (on a 100-point scale) developed by Moz that predicts how well a specific page will rank on search engines. It is based off data from the Mozscape web index and includes link counts, MozRank, MozTrust, and dozens of other factors. It uses a machine learning model to predictively find an algorithm that best correlates with rankings across the thousands of search results that we predict against.
Whereas Page Authority measures the predictive ranking strength of a single page, Domain Authority measures the strength of entire domains or subdomains. The same is true for metrics such as MozRank and MozTrust.