The two buttons can be very useful and effective.
If you setup your printer using the Page Setup and Print Settings button on the left, those settings will then be used if you select the Print button. More useful is that all of those settings are also stored in a preset, with the caveat that the printer dialog must be left to use Default. If you create a preset within the print setting dialog box, this doesn’t work as well.
so if you are using a preset, that preset includes those settings and if you hit the print button, that’s what you will get. If you use the page setup and print settings dialogs before printing even though you aren’t using a preset, hitting print is also what you will get, and you can update the preset to include the changes in those dialogs by right clicking on it
Or you can choose to use a more traditional workflow, where you worry about the print settings at the time you print by choosing the Printer ... button.
But if you create presets that don’t include setting up the print settings dialog, or you are using custom setups within that print setting dialog, clicking print won’t give reliable results because what is stored in the preset probably isn’t what you want.
I haven’t used this in Windows, so I can only assume it has similar functionality, but certainly it may work differently.
I hardly ever use the printer... choice anymore, almost everything I print is through a preset which are organized by printer/paper sizes, orientation, and paper choice. Pick the image, click the preset, position the identity plate, and click print.