A quick google search found a company that offers to create QR codes that link to Apple's AppStore when scanned on an iPhone, and link to Google's Play Store when scanned on an Android phone. So only one QR code would be needed.
Apart from that, Apple allows you to use a particular icon design to show links to the AppStore, and Google allows you to use another icon design to show links to the PlayStore. It seems they both allow you slight variations. See for example here:
https://icon-library.com/icon/download-app-store-icon-25.html
These icons are protected by copyright law and trademark law, but Apple and Google give you permission to use them. Without permission by these companies, you wouldn't be allowed to use them.
If you tried to create your own icons, there is still trademark law in your way and could get you into trouble. Because both companies will not like it if you use a different icon.