Redfish seems to be saying they are "almost" the same, but he did not say take it back for some reason. According to my looking up #10 = .190" and 3/16 (doing the math) = .1875"
I wouldn't take it back because of the few thousands difference. I would use it.
Even the correct tap or die is available in several types and grades. Send the wife shopping? Cut threads, formed threads, major, minor, pitch diameter tolerances, it can get very technical. The machinist hand book contains 100% of the related info ( and its a thick book! ) Add one of those and a few hundred dollars in measuring instruments to her shopping list? LOL
It would be nice to know where/what/when such a small bolt warrants soooo much concern.
Working on airplane engine or landing gear?