When you assign a quote to a template, then convert it to an invoice, the invoice will also follow the same template.
A few things (like the name and button call to actions) will automatically change to reflect whether it is a quote or invoice, but the deal's details on the document remain the same when converted from quote to invoice.
If you'd like, you can chose to differentiate what information displays on your templates whether it's a quote or invoice using if statements.