Hi John,
great question!
Both Terms are used nowadays.
In the past public updates were only updates available on Microsoft update – usually Security fixes and other important fixes.
A while ago Microsoft Internally this terminology was changed when the updates were released on download Center and no longer through separate hotfix Servers.
So MS Internally all These fixes are named “public updates”.
But they are also cumulative.
To avoid confusion here I stick to the term “cumulative update” whenever I talk about the monthly released fixes and “public updates” when I talk about fixes available through Microsoft update (mostly Security fixes).
Hope that helps.
Cheers,
Stefan