Do i need to run payroll when i am working on corp to corp basis?

Do i need to run payroll when i am working on corp to corp basis?

First time I am doing some contract work where the other corporation make direct payment(Direct deposit) to my Business checking account every two weeks. It's the same billing rate and same number of hours. Do i need to run the payroll to pay myself? I know I need to pay federal unemployment tax, Federal taxes, states tax(no as i am working in Texas), medicare and social security(employer and employee). I am one member LLC. The only deduction i have is the SEP-IRA. Other deduction is medical insurance which i am paying out of pocket(COBRA). 

So do i need to run the payroll? I got a payroll software which is not expensive - around $15/month -patriot software and that generate the paystub plus does the direct deposit.