It turns out that this is a rather simple puzzle to solve. Both words have the exact same meaning (a color somewhere in between black and white. :)) However, “grey” is the British spelling of the word while “gray” is a later American variant.
Some may say that if you are British you should use “grey” and if you are American you should use “gray.” Nevertheless, either is acceptable as long as you choose one version and stick to it throughout the entire length of a piece.
Other British/American differences are:
Toward (American) vs. Towards (British)
Color (American) vs. Colour (British)
Theater (American) vs. Theatre (British)
As a side note here, some writers will use the “theater” spelling when referring to a movie theater and then use the “theatre” spelling when referring to a place that houses live performances. But, just like grey or gray, either is usually acceptable as long as you stick to one version throughout an entire piece.
Analyze (American) vs. Analyse (British)
Center (American) vs. Centre (British)
Dialog (American) vs. Dialogue (British)
Another thing I found completely interesting while researching this topic is that I use a mix of both American and British spelling when I write. I will use the American spellings of toward, color, theater, analyze, and center. However, I use the British versions of grey and dialogue.
What versions do you guys use? Also, do you know about any other British/American differences?