Google maintains an internal database of PageRank values that is continuously updated as they crawl the web. If you want to call something "real PageRank", it would have to be this database. Periodically (typically every three months), Google exports this data to another database that the Toolbar uses to display PageRank values. This process can take a day or so to propagate to the various datacenters around the world. This is the only publically-available PageRank data, and every independent PageRank tool relies on this same data. The data is reasonably up-to-date at the time of the update, which is demonstrated by the fact that (with rare exceptions) new websites receive a PageRank score on the first update following their creation - even if it's shown as "0".
