Zinc gives a silver gray finish, manganese gives dark black/gray finish... Not much else in terms of parkerizing.
That pretty much sums it up. ^^^^^^^^^
You can, to a minor extent vary the dullness/shine by using different blasting media prior to dunking it.
A wire wheel finish will be a bit shinier due to fineness of surface as opposed to 70 grit which is about the norm. Be warned, the finer the finish, the shallower the park will be.
That means less oil retention ability or surface for paint to adhere.
The tiny pits formed by the media is what gives the solution surface area to react with.
A highly polished surface will likely not Park at all.