Which one fits
Order Printer is the right choice for a store that prints the occasional document, is happy with the default layout or has someone on hand who writes Liquid, and would rather not pay for something it already gets for free. It comes from Shopify, it costs nothing, and for that store it does everything needed.
Printout Designer changes how the documents are made and how they get out of the door. Templates are edited by dragging fields onto the page rather than by editing code. Documents print or email themselves when an order reaches a status you choose, so nobody has to open the order first. Label formats are ready for Avery sheets and DYMO rolls. And if the store later moves to BigCommerce, Ecwid or WooCommerce, the same setup works there too.