I don't see any misinformation here, that's an old name that got lumped with the currently accepted one. I don't think anyone's disputing the "correct" name, right?
And you have your instructions for starting those cuttings, so I'd say we've more or less answered the original poster's questions.
Fun fact: those two names were both published by Linnaeus in 1753, so they are primordial.
This plant should be relatively easy to start from cuttings (I put something very similar in the public garden). To add to the previous instructions... You don't want the cuttings (especially fresh cuttings) sitting in wet soil if and when it rains over the winter. So if you can't provide overhead protection during this time, use a smaller (shallower) pot and a rockier mix. Cold and wet is kind of a bad combination when you're trying to root cuttings.
My advice would be to water deeply after a month or two and from there on out wait for the soil to go completely dry at depth (not just the surface) before watering again. When in doubt, wait to water. When it's cold, wait to water.
Do not bury much stem (buried succulence invites rot) beyond what is needed for stability.
You might want to cut across the bottom of those pieces (using a sharp, clean instrument) in order to minimize the surface area of the cut. So cut straight across at the narrowest point. The two cuttings at the right might benefit from this kind of cleaning up.
And be patient because it does take a few years for a cutting to achieve tree-like stature.
