scripting - math.exe vs wolfram.exe vs MathKernel.exe vs WolframKernel.exe (running scripts on Windows)

I generally consider Mma documentation very good. However, it is startlingly difficult to find useful information on running Mma batch scripts, especially on Windows. So ... just what would I enter is the Wolfram documentation search dialog to fetch this information? Here are things that don't work: math, math.exe, wolfram.exe, wolfram, MathKernel, and -script. Now WolframKernel brings up a page, but it is not useful. It does provide a promising link to http://reference.wolfram.com/language/tutorial/WolframLanguageScripts.html which is not completely devoid of information but (intentionally?) does not address Windows users. Worse, it suggests that MathKernel and math are equivalent, which (on Windows at least) is manifestly untrue.

So here is what I currently believe, not from the docs, but from looking at the binaries in my Mma folder and trying them out.

• math.exe and wolfram.exe are the same and can be used with the -script option to run scripts


• MathKernel.exe and WolframKernel.exe are the same but (contrary to the Wolfram page above) are different from the other two commands in some unspecified ways and (again contrary to the page) cannot but used with the -script option to run scripts. (Or at least, contrary to that page, output intended for stdout does not go there.)

So, what are these 4 files actually, and where are they documented, and where in particular is the documentation for Windows users as to how to use them?