The about this Mac window is completely different from the one used by Sierra and High Sierra, they both have tabs across the top.
Go to System Preferences and choose Start Up disk. What does it say?
What does the background picture look like?
Doing a health check on a friends 2013 MacBook air to get it up-to-date.
Installed High Sierra because that is what I get offered when updating ( the Mac is running 10.9.5)
All appeared to complete successfully and did a Restart.
These two screenshots appear to contradict each other. I'm flummoxed.
About this Mac