The phrase "Wall Street Stock Exchange" is a misnomer that refers to Wall Street, which is in lower Manhattan, being the original home of the New York Stock Exchange. Wall Street houses many large brokerage and investment firms, according to Investopedia, making it highly relevant to the U.S. stock market.
Dictionary.com also describes Wall Street as the "financial center" of the United States. The NYSE is a market through which buyers and sellers of company shares conduct transactions on a daily basis. Investopedia points out that businesses located along and near Wall Street sometimes carry a negative perception based on the belief that they have unfair advantages in raising capital.