I have heard people call the turns of a coil “wraps”, as if it’s a tamale or fast food or something. Well, it’s not, even though that may sound delicious. Each time the wire passes through the center of the toroid core, it is called a turn, even if the wire just goes through and doesn’t wind around the core.
The toroid with no wire on it is called the core. Some people call the copper part of a wire a core, but it’s a conductor, because it conducts electricity. When you wind two wires on the core at the same time, it is called bifilar wound. I have wound 30 AWG fine enameled wire on a core with as many as five wires at the same time, which should be called pentafilar, but is probably written as 5filar. Three would be called trifilar, and four would be called quadrafilar. Winding more smaller wires onto the core instead of one big wire is easier because the wire is more flexible, which is the reason why they don’t use solid wire in the power cords, which have to flex a lot, where in the walls, the wire is solid and hard to flex. There is another good reason why more smaller wires is better but I’ll leave that for later.
The wire is usually made of a solid strand of copper, called the conductor, with insulation made of an enamel coating. The enamel coating is thinner than plastic so more turns can be put onto the core or bobbin. More turns means the core can have higher inductance. It also means that heavier wire can be used for lower DC resistance and less loss.
Using wire with insulation other than enamel coating is okay, it just means the core will not be able to have as many turns or as thick a conductor. The toroid core may not have as high a performance as one with enamel insulation. But it may be good enough for the application.
I often use wire I scrounged from telephone cables. The wire is typically 24 AWG (American Wire Gauge) solid conductor, with a coating of PVC plastic insulation. Two types if telephone wire are often available. One is called crossconnect wire, and is typically two wires twisted together. The typical colors are one is white with a blue strip and the other is blue with a white stripe. These can easily be separated by unwinding the wires and rolling them up separately, or else just leave them together and cut off a short length for use. The other type of wire is called IW, for Inside Wire. It has four of the twisted pairs, each a different color. They are covered with an outside jacket. The wires typically have a thin piece of thread which sometimes looks like angel hair, and this is used for ripping through the jacket so it can be removed. Several inches of the wire is stripped off the end. The length of IW is clamped in a vise or tied to a doorknob, and the thread is wound around the shank of a screwdriver and then pulled along the wire. As it rips through the jacket, it is wound up. Close to the end it may pull out of the jacket, but by then the jacket should also pull off the wire. This leaves the four pairs of wire bare and then they can be wound into hanks for later use.