Depending on the course, statistics (as offered by the math or statistics department) will be purely procedural. They will go into great detail about WHY you perform a procedure a certain way and, generally, will discuss theorums and formulas in detail, sometimes even proving them. There will be little or no practical application and no discussion of experimental methodolgy.
On the other hand, in a business stats course the time not wasted on in-depth detail about statistical procedures will be spent on methodology and application.
Although it will greatly depend on your college and department, some departments will waive a requirement if you have fulfilled a similar one. Usually, they will only make this exception with transferred credits (if, say, you transferred from a small college that didn’t offer a business stats course but did offer a stats course). I doubt you’ll have much luck getting them to waive your business stats course.

Here’s a quick answer to that question.

It wouldn’t be the same if it wasn’t named the same.

so if its business, its business and nothing else, then that would just be silly.

It’s business statistics because it deals with business and its scenarios and also it has specifically applied equations and theroms for business related applications as well as most of normal stats.