Other macOS installation options
When you install macOS from Recovery, you get the current version of the most recently installed macOS, with some exceptions:
On an Intel-based Mac: If you use Shift-Option-Command-R during startup, you're offered the macOS that came with your Mac, or the closest version still available. If you use Option-Command-R during startup, in most cases you're offered the latest macOS that is compatible with your Mac. Otherwise you're offered the macOS that came with your Mac, or the closest version still available.
If the Mac logic board was just replaced, you may be offered only the latest macOS that is compatible with your Mac. If you just erased your entire startup disk, you may be offered only the macOS that came with your Mac, or the closest version still available.
You can also use these methods to install macOS, if the macOS is compatible with your Mac:
Start up from macOS Recovery
Determine whether you're using a Mac with Apple silicon, then follow the appropriate steps:
Turn on your Mac and continue to press and hold the power button until you see the startup options window. Click the gear icon labeled Options, then click Continue.
Make sure that your Mac has a connection to the internet. Then turn on your Mac and immediately press and hold Command (⌘)-R until you see an Apple logo or other image.
If you're asked to select a user you know the password for, select the user, click Next, then enter their administrator password.