Domain Rating (DR) is a ranking metric developed by Ahref and shows the strength of a target website’s backlink profile on a scale of 1 to 100. However, it is not based on Google’s page rank calculations.
It is still a useful measure of gauging a website’s link popularity and its ability to get traffic from Google searches.
Domain Authority (DA) on the other hand is a metric developed by Moz that is a predictor of how well websites will rank on search engines. Similarly to domain rating, domain authority is not based on any calculations by Google but rather a useful comparative measure between websites.
Domain Authority (DA) is useful, not as an absolute measure but as a comparative measure and varies greatly from industry to industry.