Steel is rolled to make bars. Bright mild steel is rolled cold and has a reasonably bright smooth surface finish. The other type, more usually called Black mild steel is rolled when it's still very hot, which gives it a black oxidised surface.
Its easier and cheaper to hot roll, hence black MS is cheaper than bright MS.
Generally speaking, if you are going to be machining it all over, then black MS is best: it's cheaper and has far less internal stress.
If, however, you intend to use the bar surface without machining it, then you need bright MS.
If you machine all, or most of the surface of bright MS then you should expect it to distort as the internal stresses are released. This happens far less with black MS.