Ok, thanks for advice about terminology! I used the word "Base" bc I didn't want to divulge the actual name of my main drive--unfortunate choice of terms, I see now. Let's just call it "#1" from here on.
#1 does appear as one of three choices when I start up with Option key pressed. So the Installer and Recovery images are *not* the only ones that appears. If I tell it to boot up from #1 it does so fine. From what you're saying though, it default (without Option key pressed on start up) tries to start from a defective OS. Additional possibly relevant background facts:
After installing the new second SSD, the older SSD was very slow and buggy. So I restored from Time Machine to the new, blank second SSD. That also didn't work out well and so I reinstalled 10.13.6 on it (the second drive). Still wouldn't boot and so I erased everything on the second drive thru Disk Utility.
Then I reinstalled 10.13.6 on the older drive, thereby creating the current "#1." When I boot from #1 (after Options + Start), everything seems to work fine. For example, the apps on #1 seem to operate across the two SSDs without problem with libraries, such as the ones for iPhotos, that I've moved to the new one.
Is it possible that the Installer and Recovery images and crossed O are detecting problems with the OS I installed and then erased from the new disk? Thanks.