I don't have a full answer to this, just as I was curious as to where to draw the line of distinction between stainless and carbon steel. In the two examples I gave, they are vintage razors that are fairly resistant to patina or rusting. So maybe that's the difference.
The magnetic razor in question is an old Boeker that has "magnetic" etched on the blade. And the blade literally is magnetic, capable of attracting other steel. Basic honing of it took much longer than it typically would with softer carbon steel.