A Regent's diploma is one that you are awarded after you have finished high school and completed a series of exams. On the other hand, a GED is a diploma that you can get without finishing high school --- you only have to pass the GED exam to get your diploma.
Regent's diplomas require you to take tests in specific subject matter. Depending on your school district and your state, these are different subject matters. Some schools award different Regent's diplomas depending on what tests you take. Traditional tests include math, science, history and English. A GED requires one exam, which is the GED exam. This exam covers all of the subject matter that you would have been expected to learn while in high school. If you pass the GED exam, you get the diploma.
Regent's diplomas are intended to be a higher level of high school diploma for students who wish to show that they have achieved above and beyond what was required to graduate. Therefore, the score requirements on these diploma tests are higher than the usual scores needed to graduate from high school and get a regular diploma. The GED scores are a baseline assessment. These scores show that you have the knowledge required for a high school diploma. Therefore, these scores are lower than the scores required for a Regent's diploma. Both of these sets of scores and what is necessary to obtain each type of diploma are determined by your school district.
Regent's diplomas are not available everywhere. Your high school must have a Regent's program and the correct testing procedures in place. On the other hand, no matter where you go to school or where you live, there will be a testing site nearby where you can obtain your GED.