If a personal website is making revenue through advertising (e.g. Google adwords, or Amazon), as a sole-trader does any profit made have to go through the business as taxable profit?

Would there be a distinction between a personal website, and a business based website from which the extra bit of revenue was being generated, and if so, is it possible to divide the money made from the personal from that of the business for tax purposes, given that google adwords only allows the creation of one account?