What is the difference between installing zorin normally and the safe graphics mode, please explain clearly.

Safe Graphics is the same as nomodeset.
Nomodeset is the parameter that ensures that the Graphics Drivers do not initialize prior to the modesetting done by the kernel.
If the graphics loads prior, then the graphics display can crash, leaving you unable to log in to the desktop (or see it).

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"Safe Graphics" disables the GPU and instead uses the CPU to render, in case your GPU doesn't work for some reason.