The United Way receives and distributes donations on a regional basis. They tell donors they can "designate" which charity they want to receive their donation. But the distribution to the various charities is based on "budgets" developed independently from "designated" contributions. Since so few donors name a particular charity, the United Way decreases their funding from the un-designated funds....
The board determines charity X needs $100,000 this year in funding. Designated contributions specifically naming charity X come in at $20,000. Charity X receives $100,000 from the United Way, not $120,000. The designated $20,000 becomes part of the $100,000. The $20,000 in designated funding simply frees up $20,000 to give to another not so worthy charity.
The result is that the charity receives the amount the local board budgeted, regardless of your designation. So it is more accurate to say that you contributed to all the charities the United Way supports.