No I am not. I thought Matlab deals with the concept the same. Was I wrong?
An equation definition in command window should be as valid as the same equation annotation in *.m file. (perhaps )

Yes they are subtly different in a few ways. Function files (.m files) are reusable, so you can write a function and save it and call it whenever you want. You can't do that with functions you define at the command line (well you can make an anonymous function, but it only lasts as long as you have the variable around...). You can add comments to your code, debug, and do other stuff with function files that you can't do in the command window as well.

Since these equations you want to write are really comments in a file, entered as LaTeX code, entering them in the command window doesn't really work.

Well, that's the point. As you know adding a % character in the beginning of line in MATLAB, will make that entire line as a comment and will be ignored for interpretation purpose. How above sample code is suppose to define me a function where the function definition line is already commented out? That's my question I am afraid.

When you publish the file it turns the comments into HTML, so the equation renders and displays. The m file is just the source file that is published to produce the final output

Just to be clear, you can't import an equation into MATLAB as a usable function from math type. You'll need to do that manually by writing the expression out (or use an anonymous function). The functionality described above allows you to display the same equation as an annotation.