There is not much difference between environmental science and sustainability studies. But still both the courses should not be confused with one another. Environmental science generally refers to the subject matter which involves the study of chemistry, ecology, environmental engineering and hydrology. It also teaches you about issues of pollution, water cycle, mitigation, etc. One thing which is should be considered is that; never confuse environmental engineering and environmental science.
On the other hand, sustainability studies refer to the bottom line of society, economy and ecology. It is a mixture of subject matter related to environment as well as physical sciences and policy and social sciences. The people who do a PhD in sustainability studies or an online PhD in sustainability studies go through all these relative subject matters. Sustainability studies are broader disciple. It may also include materials of environmental science.
It entirely depends on the educational institution what it wants for their students to study in the respective courses. Some of the best business schools in Switzerland offer these courses as a major to the interested students. The syllabus and the study material are decided by the universities and thus it differs from one institution to another.