English Grammar is a set of rules describing the properties of the English language. But Academic English is the English language ability required for academic achievement and purposes such as Engineering courses.

As indicated by Mahmoud, Grammar is merely the rules for English. Academic English is the more advanced vocabulary as used in College-Level correspondence, Scholarly Communication, or the language of Business, Law, Philosophy, Theology, Science, the Arts, and so forth and so on. Personally I think good speaking skills should be mastered before trying to integrate an advanced vocabulary. When I introduce my own "advanced vocabulary" to students, the thoughts conveyed require careful study. Also, I think that the student makes great errors in thinking, if they suppose that learning "advanced vocabulary" is a process of merely adding individual words. The true skill in learning English Language, appears in the student's apprehension not of mere words or phrases, but in the comprehension of entire Ideas. A student can be said to have actually "mastered" English, when they can grasp broad conceptions as written in published works. This is not the kind of English that appears in ordinary conversation. "Academic English" involves the development of critical thinking skills and an appreciation for certain principles that apply to disciplined fields of human knowledge, as enumerated above.