Backlink is a link from an external page or website which refers to your website. This tool checks number of backlinks of your website. As search engines give different results, so value in this tool will also fluctuate, based on your IP and search engine.
PageRank is a link analysis algorithm, used by the Google Internet search engine, that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. This tool checks Page Rank of your website.