Your links all point to a threadless stem. If you were intending to point to something like
this:
Quill Stem adapter
What that bike has is a threaded headset, that works with the steerer tube on the fork to provide a bearing for the fork to turn. The difference with a threadless headset is that the steerer tube is threadless, and the stem clamp, spacers, and top cap work together to preload the bearings (eliminate play), and then the stem bolts are tightened to lock that adjustment in.
In your case, switching between the two is close to impossible without finding a 1 inch threadless fork and headset to use. That's why the quill adapters exist. You insert it like the original stem, tighten the stem bolt and binder in the steerer, and bolt the stem onto the new 1 1/8" clamping area at the top of the adapter. The good news is that this will allow you to utilize modern handlebars with the new 31.8 mm clamp diameter, the bad news is that it's not very aesthetic.
If it gets the bike back in use though...