My understanding, now:
A rack or single tooth acme shaped cutter on a shaper can cut an ordinary spur gear to an involute profile by rotating the work on its shaft axis and faceting the tooth. It will always be a faceted tooth -- the more strokes per tooth, the more facets, and the finer it can approximate a smooth involute tooth form. This is illustrated by the rig that Matt linked.
A horizontal mill cutter of the rack form can do the same thing faster for the same number of facets, assuming it has more than one cutting tooth. Or cut more facets in the same amount of time, for a finer approximation of an involute tooth form.
In general, the rack shape is easier to form if making a cutter from scratch than a involute profiled cutter. And one rack style cutter serves for all gear tooth numbers, while an involute profiled cutter is suitable for only a range of gear teeth numbers and the actual tooth form cut is approximate.
A hob suitably geared to the work arbor and placed oblique to the work can be arranged to produce an un-faceted (smooth) involute profile because it acts like a continuously variable cutter. J Radford once did a lathe attachment that performed this way. As I visualize it, the tooth won't be completely uniform across the gear, but the profile will be involute at any particular cross section.
Moving on to bevel gears, a hob is not possible because the gear teeth converge.
A single tooth cutter can not be designed to cut a good involute bevel tooth on both edges, no matter how it and/or the work is rotated and translated. And no matter whether the tooth is involute profiled or rack profiled.
It can be designed to be narrower than a bevel gear's tooth, so that it cuts on only one edge, until rotated and translated to cut on the other edge after the prior pass. This is the principle of specialized involute profiled bevel gear cutters. As illustrated by the video Joules linked to earlier.
These work by first clearing the center space of a tooth cut, then they are rotated and translated to widen and shape that same space on first one side, then the other side, yielding 3 passes per tooth cut. Being involute profied cutters, they also only work with a small range of gear teeth numbers so must be available in sets.
The final possibility, and an interesting one for a home workshop bevel gear cutter, is using a rack form tool either in a shaper or mill. A multi toothed mill has the advantage, as usual, of speed, as this method will also create faceted teeth, and the more facets the better the profile, but the longer it takes to complete a tooth.
If I simplify the machine concept, just for visualization's sake, to a fly cutter of rack shape, I can imagine having a horizontal mill spindle which can be positioned around the vertically oriented gear tooth being cut, with the cutter arranged to spin tangential to the bevel gear's tooth cone. And to cut along that axis. It would have to be narrower than the tooth space. As before it would cut only one facet on one tooth face at a time. Multiple passes per tooth side would be required to generate a faceted involute form.
How to move that mill spindle mechanically, vs via cnc and an equation is an interesting puzzle I'm still thinking about.