For the future benefit of anyone who happens across this thread, and is as baffled by it as I initially was...
When Windows 98 Second Edition was released, Microsoft issued both upgrade and update versions of it. The update one only worked if you had Win98 First Edition installed. The upgrade one worked if you had ANY Windows versions earlier than Win98 Second Edition installed (i.e. whether you had First Edition, or Windows 95, or Windows 3.1).
In both those cases, you ended up with Windows 98 Second Edition.
So if you're currently upgrading from Win98 first edition, there are two safe ways to do it: you can safely use either the upgrade CD or the update CD.
However, the upgrade CD was not intended to be an upgrade from Win 98 first edition, only from Windows 3.1 or Windows 95. If you have 98 first edition, you have to rename the file WIN.COM (which is all that the installation program looks for), thus fooling it into thinking that you've actually got Windows 95 installed.
So boot into DOS, and rename the file WIN.COM (in the directory C:\WINDOWS), before you start. It doesn't matter what you name it to (try naming it WIN.OLD as most people used to do).
If you buy the full install CD, which is the third product Microsoft used in launching Win98 Second Edition, that version deletes your existing Windows installation (the folder C:\Windows and everything in it), and installs the new version: thereby deleting all your customized settings, instead of preserving them.
This is how you get a clean install (which you might want if you have a badly corrupted or damaged installation of Win98 first edition). Once again, because you already have a version of Windows installed, you fool the installation program into thinking you have NO existing version of Windows, by renaming the file WIN.COM (as above), which is the only file the installation program looks for.