There are many diamond grading systems in the world. In North America, the most respected ones are the AGS (American Gem Society) and GIA (Gemological Institute of America) systems. They qualify and quantify grades with specific and accurate terms detailing the grading factors for a diamond. (Of course the most important grading factors, the 4 C's).
The most notable difference between the two is that the GIA report for any given diamond does not include a grade for the cutting of the diamond. It contains some, but not all, of the key geometrical statistics that can be used to understand how well the rock is cut. (See our "Cut" section for more details). For a sample, and explanations, of a GIA report, click here.
There is a difference between a GIA certificate, and an appraisal done by a GIA Graduate Gemologist. What you want is a GIA certificate, which is expert opinion given by an independent, third party. A GIA Graduate Gemologist title merely means that he/she received education from GIA, but he/she might be affiliated with a jeweler, thus might not be giving unbiased advice.
Other certificates, like those issued by the labs EGL (European Gemological Laboratory) and IGI (International Gemological Institute), could also be available from a jeweler. These two labs are regulated by the Federal Trade Commission (as is GIA ), but somehow are less common and to some people, has a reputation of being a bit laxer in their grading.