I would like to know why only one of my client invoices prints a 'Pay Invoice' button if I do not have online payment options enabled.

Your invoice template in QuickBooks Online (QBO) seems to be a customization. I'll explain this more for you to understand.

When use the custom/old template, the Pay Invoice button will show on the invoice PDF. If you prefer this option to be hidden, you'll have to switch to the Modern template. I'll show you the steps:

1. In QuickBooks, go to the Sales.
2. Select the invoice you want to modify and Edit.
3. In the left panel, choose Design and click Modern for the Recommended template.
4. If done, you can Save it.

On the other hand, see these articles as an additional guide to handling invoices in QBO:
 

• Record invoice payments in QuickBooks Online
• Customize invoices, estimates, and sales receipts in QuickBooks Online

After that, if you still have questions about managing invoices or any other QuickBooks-related concerns, let us know. We'll be there to assist.