I distinctly remember one of those words is a person’s last name and the other a color. It’s a major faux pas to send a memo to Mr. Color. Getting it right is important in the office. I’m pretty sure Gray is the name but wanted to check.
The internet claims one word fits all. That’s not correct unless something has changed in the past 45 years.
Whats the Straight Dope?
As far as I know, either spelling is the color. I think GREY is used more by the British and the US uses GRAY.
Edit: NOW I have read your link and it says pretty much the same thing.
A simple search in the phone book shows that the internet is right.
edited to add: Wiki link on colour spelling.
As far as I’m aware, both spellings have been exactly interchangeable for each other for the color name. Probably for many centuries.
As for the surnames, both spellings are well-established surnames, neither one being “correct” while the other is “wrong”.
Your link answers the question for the color. If it’s a person’s name, all bets are off. One of my family surnames is Gray, but there are tons of Greys out there as well.
I wish the internet had been around in 1969. My elementary school teachers insisted on using one word for the color. I just can’t recall which. 
Heck it was a standard question on our weekly spelling quizes.
Stupid teachers and their rules. My way or you fail.
There is a whole website dedicated to this conundrum. The website agrees with I. Dunno. It is mostly US vs. England with respect to the color. There are people who spell their name Gray and some whole spell it Grey.
Grey is simply the proper way to spell the word that describes a the colour between black and white. The US spelling variant showed up in Webster’s dictionary in the early 19th century - http://books.google.ca/books?id=twC-H4a8VcYC&pg=PA282&redir_esc=y#v=onepage&q&f=false
Both Grey and Gray are used as last names.
You’ve been waiting for this moment for 12 years, haven’t you.
Or you’ve just been wrong for 45 years. And that’s not a personal dig, teachers screw up all the time and teach kids falsehoods, or they oversimplify thinking that kids will figure out that life has more “gray areas” (pun intended) later in life. I’m still unlearning stuff I was taught as fact in grade school. I remember being taught that “grey” was British and therefore was as incorrect as “colour,” but then I got older and discovered that both were fine.
The way to check, as with any name, is to call the person, the assistant, or the company receptionist and double check. The major faux pas is to believe that the spelling of a proper name follows any kind of rule.
“A” proper way, not “the” proper way. Both “gray” and “grey” have equal standing, just as “colour” and “color”. Seniority doesn’t matter a whit, even whenit can be conclusively established.
Without researching, I bet “gray” has a very long history.
The proper way. I mean, would I lie? 
Just waiting for the deep debate on why anal probing is a completely legitimate branch of xenobiology and then I can finally stop posting.
Niiice!
Paul Simon said it best.
When I think back
On all the crap I learned in high school
It’s a wonder
I can think at all
Personally, I think of “gray” and “grey” as being two subtly different colors. This is doubtless due to my early reading of Tolkien, Lewis, and other British authors: The sorts of things they refer to as “grey” tend to be different from the sorts of things boring American authors refer to as “gray”. So, grey is the color of wisps of fog blowing in from a haunted moorland, or of a wizard’s beard, but gray is the color of a T-shirt that’s been accidentally washed in with the dark laundry.
OED page for “grey|gray” with historical citations. Run a find on the spelling “gray”, and find the many dozens of cites from the fourteenth and fifteenth centuries, a few of which predate The Canterbury Tales.
And you’d be right:
[QUOTE=OED]
The variation between spellings in ei, ey, etc., and in ai, ay, etc., in later Middle English results from the general Middle English merger of the ei and ai diphthongs. . . The present word is distinguished by the fact that both spelling types continued in frequent use for a very long time, and different spellings have been selected as standard in U.S. English (gray) and in British English (generally grey, although individual usage can vary).
[/QUOTE]
Edit: damn you! In the time I spent putting the italics back in, you posted the link.
Thanks for the backup all the same 
Surely grey is the colour, whereas gray is the color?