I can't speak authoritatively, but I do have all three types and have had good luck with my seasonings, so I'll share what I do.
For cast iron, I use solid vegetable fat exclusively (Crisco). I did the original seasoning by coating it in fat and baking in the oven. To clean it, I use salt, Crisco and a paper towel to get any food bits off. I then get the pan hot and wipe it down with a little more Crisco. It's not PTFE nonstick, but pretty good.
For my forged iron DeBuyer fry pan, I followed the manufacturer's recommendation for initial seasoning: put enough oil in the pan (I use canola) to coat the bottom. Heat to smoking. I swirled the hot oil around to coat the sides a bit. Let it cool, pour and wipe out the oil.
The thing I've found is it takes quite a bit of use to develop the seasoning. Here's a picture after about a month's use - note how dark the sides are getting (the bottom is less dark because I learned a green scrubby pad (Scotch-Brite) will remove the seasoning entirely. Oops!).
I did some scrambled eggs for the sake of science, without adding any extra oil to the pan. They behaved as nicely as any PTFE coated pan I've ever used.
Today the entire bottom of the pan is that rich mahogany color, and a fried egg slides around in it like one of those goofy AS SEEN ON TV ads.
EDIT: Used the pan for over easy eggs this morning and snapped a new picture. This is about 3 months after the last photo.
Normally I can just wipe it out with a paper towel. If I've been cooking bacon or something that left residue, I'll run water into the pan while it's still ripping hot, then wipe it out gently with a sponge.
After that I heat the pan up and add just a tiny bit of canola oil. I wipe the oil around with a paper towel and put the pan away.
For carbon steel--like my wok--I treat it exactly the same as the DeBuyer pan. Clean gently, after each use get the pan ripping hot and wipe it down with some oil.
If all the seasoning is completely removed, it will look shiny like brushed or polished metal. This takes a lot of time, and often power tools. I would first ask whether this is what you want to do: does the pan feel waxy, and have a surface that turns glossy when heated? Then there is wax which can be easily removed with a scrub-brush while water is boiling in the pan. Finish with a little soap and hot water, and you're ready to season.
If it is, in fact, the seasoning you want to remove (if, for example, it is coming off in places, or parts are rusting, typically on cookware which has been left outside), the easiest procedure is to heat the pan very hot, either in the coals of a campfire, or in an oven on 'clean' to burn off the previous coating (don't do this with a pan coated in wax, the wax will burn and smoke), then brush with steel wool until the metal pan starts to show through. You will need to season with several coats of an oil like crisco or coconut, and this will take a lot of time. It's rarely necessary to strip a pan unless it is in awful condition.
At the point you're at, I'd assume that any wax or residue is gone from your work with the steel wool, and that you don't need to go as far as to strip the whole thing. To salvage it, put aside the steel wool, scrub with a plastic brush and hot water until the black residue is gone. Clean a little more using a rag and oil (which will pick up oil-soluble debris) until that is clear. Then season as you normally would, using a light oil like crisco in the oven.
Best Answer
Just a note that if you use flax seed oil to season, it is notorious for flaking later. Also you may be seasoning with too much fat/oil when you heat it to create the polymerized surface.
The way to season carbon steel, woks, and cast iron is to wipe oil in the pan then wipe it out so that you can barely see a sheen of remaining oil. THEN heat it to the smoke point and let it fully dry and repeat, repeat, repeat! Again, when you first put in the oil/fat, you MUST wipe it out. That will allow for the polymerization to work as intended and not leave a surplus, sticky, or exessive quantity that doesn't complete polymerization with the pan in full.
Bon appetit!