A DIK can be made to a DAF, or a DIK can be made to the church.
The DIK has to be one year old in order to receive the tax benefit. The DAF and the church are charitable organizations. The DIK is the charitable event. You could also use cash and donate to either the church or a DAF. You either make the donation to the DAF and then send the funds to the church, or you make the donation directly to the church.
Once you send the money to the DAF, it isn't yours anymore. It is the charity's money. They let you suggest who you donate it to, but there is no additional deduction at that point.