Thank you very much.
I read your email above and went to implement the recommendations in the article to which you linked me.
The synch had already occurred overnight. I think!
One puzzle remaining is what is this process of swiping down through the contacts? I tried to do it and didn't feel as though I was swiping. The contact names just swirled down in the same direction.
However, to test whether synching is still happening, I went to my own contact page and made some trivial changes in the notes section and then looked at the other device and the change had been implemented by the time I got Contacts open on that device. And in the opposite direction, I changed things on my contact card on the other device and those changes showed up immediately on the first device.
Before I noticed that the two devices seemed already synched, I did check the Apple ID on both devices. I also changed the green to white on Contacts in iCloud and back again. I also completely closed Contacts and reopened it again. All things in the article. So, it is likely that something from the article did work but I wasn't immediately checking to see which adjustment might have caused synching. But now it appears that the two devices are synching immediately which is exactly what I wanted to do.