Thanks for moving this to a more appropriate location!
Two things to add here:
1. I remember now that this has occurred before. On that occasion, and again on this one, when I actually did "click to update" I was sent to a Microsoft FAQ information page that told me how to install the Creators Update (version 1703, which has been installed and running on both machines for quite some time now). The assumption seemed to be that I had not yet been auto-updated and that I wanted to know how to "jump the queue". The information presented was so obviously inappropriate that I backed out immediately.
2. The Avast Premier software updater reports that all software is up to date.
And, once again, the "Patch Tuesday" update was successfully processed by both machines last Tuesday evening. After completion, and still today, Secunia PSI continued and continues to report that Windows 10, and both versions (32 and 64 bit) of Internet Explorer 11.x, are in need of manual updating.
Speccy reports as installed on 8/9/2017 the following "hotfixes" on both machines (and no install failures)
KB4034674 - the August cumulative update - for version 1703 64 bit
KB890830 - the Malicious Software Removal Tool - ditto
KB4034662 - Security update for Adobe Flash Player - ditto
So am I correct in thinking this is a bug of some kind in Secunia's detection of the Windows update status? - and that it will sort itself out at the next update cycle?
Thanks for enlightenment!
I had understood (please correct me if I am wrong) that with Windows 10 and automatic updating, I no longer needed to worry about Windows Update (I well remember its operation in earlier versions of Windows).