Proper way to run a Mathematica script (-script vs -run vs MathematicaScript vs <)?

I'm not sure on which operating system you are and whether this makes a difference, but your 4 choice don't do the same.

math -run file.m

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edit:

When you change this command to math -run < file.m then it does the same as the next (wrong) alternative.

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Doesn't do anything with the content of file.m at all, because the -run option expects a command like math -run Print[2]. Additionally, the command is not ran in batch mode like you would expect it from a script. Instead, an interactive command-line Mathematica session is opened. This is the same (although the session is quit instantly) for

math < file.m

where the content of file.m is executed, but file.m is not considered to be a script. You can easily see this when you create a script file with she-bang like

#!/usr/local/bin/MathematicaScript -script

Print["Hello"]

the the output of math < file.m looks pretty awesome:

Mathematica 10.0 for Linux x86 (64-bit)
Copyright 1988-2014 Wolfram Research, Inc.

In[1]:= 
                                #1!
Out[1]= -script + -------------------------------
                  bin local MathematicaScript usr

In[2]:= In[2]:= Hello

In[3]:= 

Your last alternative seems to miss the -script option which is (as stupid as this may sound) required, even for the MathematicaScript command. Therefore, I need to run

WolframScript -script file.m

or I get an error

error: Need to provide the -script option. Usage: -script

which is pretty lame.

If I had to give a suggestion, I would tell you to always include the she-bang in your file and make the file executable with chmod +x. Then you can simply call

patrick@lenerd:~/tmp$ ./file.m 
    Hello
    patrick@lenerd:~/tmp$

From my experience and under linux:

For MMA v10, I use:

MathematicaScript -script script_file

For MMA v11, I use:

wolframscript -f script_file