Plasma is when the electrons are "freed" from their host atoms for a short time, due to high temperatures. Fire is plasma, it responds to electric fields. Lightning is also plasma. When a column of electrons flows from sky to ground, the air that it passes through lights up with energy. What we see as lightning is actually the air where the electrons are at, getting excited and giving off light. Not the electrons itself. Lava refers to molten rock. Molten. Liquid. Not ionised gas. It's a plasma when it's ionised gas, nobody cares about temperature. If a gas can be ionised (IF) at -100 degrees Celsius, it's still called plasma.
When a connects to an power supply, an flows from one metal to the other. As the travels through the wires and the filament, the heats up to the point where it begins to emit photons, which are small packets of visible light.