Delivery fees are handled differently by different owners. Some owners keep the fee, others give it to the driver, some split it in various ways. If the driver is driving his or her own car, the store can reimburse the driver for that use, the reimbursement (subject to some rules and limits) is deductable as an expense to the business and is NOT taxable to the driver. If the store reimburses for vehicle expenses and gives the driver the delivery fee as compensation, I would suggest you talk to your accountant. Most likely it would be considered compensation to the driver and be taxable to the driver and subject to withholding and matching contributions from the business.
Tips are taxable earnings for the driver and you give them to the driver. Some businesses will pay out the CC tips that day, but I think more add them to the paycheck. You need to declare them as income and wages and matching withholdings are taken from them.
I am sure others will chime in but here is how I do it:
Delivery charge: This is my money. It is an income category, it goes to the bank. If the driver is driving his or her own car, I pay them 6% of deliveries as “mileage”. The number is not connected to the delivery charge, but the delivery charge does help to offset it.
Tips: We do not take CC so I do not have your specific issue, but since I pay $6 to drivers which is below minimum wage now, the drivers to have to declare tips. In our case they are all cash not CC but the effect is the same, taxes are withheld and the appropriate things like FICA paid by the busines.