No relation. A neon light is plasma: charged particles in low pressure or even vacuum. In a neon light the particles are molecules of gas. In space they might be molecules or dust particles.
Fire is a chemical reaction between a fuel and an oxidizer.
Don't talk about plasma around astronomers. They get really rude.
Here is a flood of plasma science: https://www.thunderbolts.info/wp/daily-tpod/
Not Sure 