Ok.. someone has already mentioned this, but I will re-iterate...
The different types of materials are:
*Kanthal (Iron, Chromium, Aluminum)
*Nichrome (Nickel, Chromium)
*Stainless Steel (Iron, Chromium, ??)
Titanium
Nickel
The First two, Kanthal and Nichrome are alloys specifically designed for making heating wires. They are a mix of metals that when electricity is applied, turns the resistance into a heat while maintaining a general form. Those two are used specifically for Variable voltage and variable wattage ecigs. Read further to figure out why.
Stainless steel is a mixture of Iron, chromium, and other alloys depending on the grade of steel. For example, 304 stainless is iron, %18 chromium, and %8 nickel, whereas 410 stainless steel contains iron, 17% chromium and no nickel. It conducts electricity much better than the kanthal or nichrome wires, so if it's used in a variable wattage device, It is pretty assured it is a subohm build.
Titanium and Nickel are base metals and both can be found on the periodic table. They are not mixtures of metals. Because of this, if you have a nickel or titanium wire, It should heat up the same from one manufacturer to the next. As these metals heat up, the resistance to electricity goes up in a very predictable manner. So, the ecig should know how hot the wire is by remembering the beginning resistance (when cold), applying the current resistance once electricity is applied (hot) then figuring out how hot the wire is by the difference of those two. It doesn't actually measure the temperature of the coil, instead it figures it out by knowing how much resistance the wire is given.
Now, the three with an astericks are alloys, or mixtures of metals.. they a generally are used in Variable voltage/wattage devices.. the only wildcard in the bunch, is Stainless steel. It's resistance profile doesn't change that much when heated, so people have been using them in Temperature control mods as well. The general vaping community has decided on 316L which is a low carbon version of the typical 316 SS. The wildcard is when someone decides to use a different grade of Stainless Steel.. who knows what will happen.
That page you linked looks confusing... What I just posted gives you an idea of what is used where.
Now, for my own opinion.. I stick with Kanthal for the most part. I do have some titanium and Nickel, but I prefer the nickel for temperature control. Titanium when overheated can cause Titanium Dioxide. Titanium dioxide, while mostly harmless, has been shown to cause respiratory tract infections in lab rats WHEN INHALED. Even though there's not much evidence that it is harmfull besides that one study. The manufacturers of Titanium Dioxide powders used in cosmetics hasn't shown any increased risk of cancer due to occupational exposure, so I am sure the miniscule amount that MIGHT occur on the coil is next to nothing compared to what they go through. The only reason I don't like it, is I am suspicious of the wire I have now.. my fingers turn grey when handling it, so there is some sort of substance on the wire itself. Whether or not it's oxidation, I have no idea... so, I stick with nickel. But I'd say I am %95 a kanthal kind of guy.
sorry for the rant...but I hope this helps explain it.