Variable behavior at startup

When logging on after sleep or logoff or shutdown, I get a gray screen with spinning wheel and sometimes a spinning color wheel as well. Usually this will be followed, after variable duration, by normal-appearing desktop screen, but it takes longer. This also associated with occasional unprompted shutdowns necessitating restart, unsure if related. Main concern is reason for dual startup wheels; do they signify a problem? running Catalina 10.15.2, update pending, behavior predates last upgrade. Device is iMac late 2013.