Many thanks for the very clear reply!
In my case, I was trying to download - indeed DID download ..several times - the "deprecated" (i.e; vintage, no longer supported) Java SE 6 "Runtime" version so that I could use Blurb's "BookSmart" picture-book editing software, but none of the Java SE 6 versions - whether from Apple's site nor from Oracle's own site - got BookSmart working.
The helpful people at Blurb's helpdesk pointed me towards the same Apple download site as described in this thread, but when BookSmart STILL didn't work, they sent me a link to the Java 6 SDK (Software Development Kit) which I downloaded ..and then everything worked perfectly!
So in this case I got a message from the Operating System telling me to download the "runtime" version ..but what the program actually needed was the full SDK version! With that installed, I've had no further problems.
So with BookSmart Java SE 6 runtime isn't sufficient; the SDK is necessary ..and perhaps that's true for some other programs which may need the "legacy" (i.e; "old") Java SE 6 SDK version in order to work.
Many thanks again, yours, David.