I have noticed that in NYU, there is a LLM for international legal studies and an LLM-SJD for international law and comparative law...

Could anyone tell me what is exactly the difference??

The LLM-JSD is a structured program designed to help you come up with a good, workable thesis for the JSD component of your program. You should be able to find the necessary information on the NYU website. You also need to do extra writing and attend the IILJ colloquia in your LLM year.