you will NOT have the same results, but both results have their own interest.
In the first case, the buffers will not overlap. So the total area under the multiple ring buffer will be equal to the area of one large buffer. This is usefull if you want categories of distances (e.g. how many inhabitants are between 1 and 2 km away from an hazard). Note that, if you simplify the shapes (which is usually the case with buffer because of the necessary rounding, this might slightly affect the precision of your buffer, but this will most of the time remain unnoticed)
In the second case, the buffers will overlap, so the total area under the multiple ring buffer will be larger than the area of the large buffer. This can be used for multiple neighbourhood analysis (how much resource can you find within 5 km?). Note that you can erase the inside buffer to create the ring after creating the buffers, but this is an extra step.
As I said, there is no better or worse result. In my opinion, overlapping buffers are more useful than the rings, because I prefer to use continuous euclidian distance raster than a large number of rings.