How do I create a client invoice vice customer invoice?

There is no such thing as a Quicken "client" invoice.

Quicken knows of two basic invoice types: customer and vendor. That can't be changed.
But when an invoice is printed, it only says "Invoice", by default.
You can change that part of an invoice (it's called the "Title") - if that's what you want to do.

Business > Invoices and Estimates > Design Invoice Forms.

I suggest you keep the "Default" invoice layout as is, and create a new invoice layout for Client Invoices (I believe that Vendor invoices always use the "Invoice Default" layout).

So: click Layout > New and give the new layout a type of "Invoice" and a layout name (Client Invoice, if you like).

Locate the text "Title" in the green bar on the left side of the layout form, and click on the double-arrows to its right. That should open a small dialog for "Title of Layout". You can change that Title text to read "Client Invoice", for example. "Title" is different than "Name", though they can both have the same value.

Keep track of the name of your new layout; then make sure that layout is selected when you create a Customer invoice.