There are various wiretypes or combinations of wire that can be found when buying stock coils, premade coils and wire for DIY. Exotic coils have more nooks and crannies to saturate with ejuice and a bigger mass so they need more power to heat up.
Round, most commonly used, simple to work with. It comes in different gauges and can be used to create exotic wire types.
Flat or Ribbon, essentially the same as round wire, but flat. This creates a bigger surface area.
Twisted, a combination of 2 or more round or flat wires twisted together.
Clapton, one core round wire is wrapped with a thinner round wire (similar to a guitar string). Fused claptons have 2 core wires.
Alien, these are similar to claptons, there are core wires that are wrapped with an outer wire.The thinner outer wire is wavy because it's de-Claptoned. This means that the wrap wire was taken from a Clapton and Claptoned again in reverse.
Framed, when the inner wires used for a clapton consist of smaller wires sandwiched by bigger wires. They are then claptoned with a thinner outer wire.
Staggered, clapton wire where 2 outer wraps alternate.
Staple, flat ribbons stacked together and then wrapped like a clapton.