Hello,
Google Rank
This is perhaps the most easily understood. Google Rankings is something of a colloquial term that refers to the position your website appears on a Google Search Results page for a given term. For instance, your website may place 5th for "Best pancakes this side of Texas" or 28th for "best food in America". A search results page is sometimes know by the acronym "SERP" (search engine results page).
Getting a site to place highly for a number of key phrases is what
SEO and SEM is all about. The quality of your content, the structure of your website page, your keyword density, the number of quality links to your content all play a part and this is discussed at greater length in many other articles.
Google Page Rank
This is a very specific metric that applies to each page of your Web site. It is a number between 0 and 10 thought to be exponential (so 4 is ten times better than 3) and it is generally believed known to be influenced by:
The number of websites that link to your site
The reputation of the website linking to your site
The relevance of the content between the two sites
Your home page will typically receive the highest page rank number and this will then "trickle" down through your other pages, diluting to smaller values as you get deeper into the site. You can view the Page Rank of any webpage on the Google Toolbar that you can install into Internet Explorer.