a 'variant' is a form or version of something. Variants differ in some respect from some standard, and from each other. "favor' is a variant form (American) of the British word 'favour'.
a 'variable' : some factor which can show changes in its quantifiable measurement. For example, to predict the weather tomorrow, the meteorological bureau takes into account the variables of wind direction, wind force, cloud density, cloud type, temperature etc.
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