I am having an issue marking my invoices as paid and not closed. What am I doing wrong???

It seems you are referring to the Payment status located in the All sales section, @frostworks. I'll help explain why you're seeing some transactions with the status Closed, and others as Paid.
 

When you apply a payment to an invoice in QuickBooks Online, your transaction will officially have two parts, which is the Invoice and Payment. The Invoice is what gets marked as Paid, and the invoice Payment is what is marked as Closed.

You can refer to this article to to keep track of your customer's payment: Record invoice payments in QuickBooks Online.

Additionally, check this article to keep track for all of your recorded transactions in QBO: Record and make bank deposits in QuickBooks Online.

Moreover, you can maximize the efficiency of your financial processes by collaborating with our QuickBooks Live Expert Assisted team. They're veterans in the field, known for smoothing out financial operations and offering insights tailored to your business. One click connects you to a more prosperous financial path.
 

If you need further assistance with managing your transactions in QBO and effectively track your business operations, click the reply button. I'm always here to help.