The Epson app seems to have colour settings as shown on their website https://epson.com/epson-print-layout – whereas Affinity doesn't have this options. So it appears hard to judge whether the "print settings for both apps are identical". On mac the difference might be caused by macOS which prefers using its driverless Airprint technology and thus does not transfer possible options of an Epson printer driver to Affinity. As workaround you can try to install another virtual printer but