No, an expense write off is not the same as a deduction. Yes, any business can claim an advertising expense, but it does not have the same tax benefits as a charitable donation. Advertising expense is no different than buying toilet paper for the office crapper. It's an overhead expense.
Not trying to start a war here, but unless you can give me some specific example, I don;t think you know quite what you are talking aobut. For most businesses, there is no true distinction between "ordianry and necessary' business expenses and charitable contributions. TEhy both lower your taxable income. If anything, a charitable contribution may, in some circumstances, be less benficial to the donor than an advertising expense.