PageRank is an algorithm created by Google founder Larry Page, and named after him. It’s a simple measurement of links and link equity. Google looks at a given site and measures the number of links pointing to that site. It measures the authority of those sites as well, to prevent abuse from link farms. A site with higher quality incoming links in a higher number will have a better PageRank.
Domain Authority is a metric created by Moz.com as a more accurate indication of the value of the site. Like PageRank, it is a logarithmic calculation of the authority of the site. Rising from a low 30 to 35 will be easier on this scale than rising from a high 80 to 85. A DA of 100 is the top ideal, while an unranked site would have a DA of zero.