I don't understand why you would set your WB to a gray card. Is this to make for a different feel to the image?
No. Either white or gray can work, but the WB idea is a neutral color (but not too dark is a good idea too). Pure gray is a neutral color, not red, not blue, i.e., no color cast (but random grays certainly can have a color cast too - there are pink grays and blue grays, etc). Neutral gray has equal RGB components, like RGB (50,50,50) or RGB(150,150,150) are neutral gray. White and black are just special cases of a gray tone, black near RGB(0,0,0) and white near RGB(255,255,255). This shade that we see in our picture depends entirely on how much we light it, but the neutrality should remain.
Except the color of light varies. Incandescent is orange, skylight is more blue. Different instances of any of them vary, flash varies color with power level. This non-neutrality gives a color cast to all subjects in that light.
Our white balance tools (today's variety) watch us click on a neutral spot in the picture (a white card or gray card). That is how we tell the computer that "this spot is neutral, make it be neutral". And it does, it removes any color cast there, and leaves it neutral (equal RGB). Which we know it should be... so that ideally corrects the whole image perfectly.
Even black can work, but a dark color like RGB(40,40,40) is too near zero to ever be able to show much of a red cast. It can sort of work if no other choices, but lighter, towards white, is the best bet, shows the color cast better.
Gray cards for white balance are nowhere near as dark as 18% (and 18% cards are not color controlled anyway). Still though, better than nothing. Even scene stuff we find in the picture can work, white plates, envelopes, church steeples, picket fences, shirt collars... maybe not precise, but all normally much better than nothing. But a good known white card is best.
One example of this variety is at
White Balance Correction, with or without Raw
One consideration of white is we cannot let it be clipped at 255, because if one channel is clipped, we lose our color cast, so there is no clue how to correct it.
But a white card in a portrait scene probably does not reach 200, because we cannot light humans that bright either.
My notion is the white card is about perfect. No gray pigments for manufacturing to have to control either. I have a couple of WhiBal cards, but I prefer to use the Porta Brace White Balance card ($5 at
B&H).