App store says I have recently updated High Sierra but appears I'm still on Mavericks?
The App Store screen only say what you have downloaded, not installed. 

Check if the download file is still on your hard drive named "Install macOS High Sierra" in your applications folder. 

If Yes double click on it and it will start.

Once the install was successful the install file will self destruct.

Because of that I usually make a copy of it before it self destruct, so I can create a bootable USB later (when I have time for it). = Procrastinating :)