A friend stated that stars are hot balls of gas, however we know that technically stars are plasma. Is his statement entirely incorrect? Can a plasma be considered a form of gas or should be referred to as a distinct form of matter?
Good question! The defining difference is that in a gas the atoms are intact, and in fact are typically bonded into molecules, whereas in a plasma at least some of the electrons separate entirely from their atoms. In other words, particles of a plasma are charged, but particles of a gas are mostly uncharged. So technically, a plasma is not a gas and it should be said that a star is a ball of plasma, not gas. (Actually, there is a thin outer layer called the photosphere which actually consists of gas because the temperature isn't hot enough to form plasma)
However, outside of physics, people often use the word "gas" to refer to any sort of vaporous substance, and in that sense I suppose a plasma counts. So there is a sense in which your friend's statement might be considered correct. But that's a question for the English site.
Gases are very simple systems. Just consider a hallmark of all gases, the ideal gas. There are no interactions among the particles there. The real-life gases do have some interactions but these can be treated as perturbations of ideal gas. Of course, at certain portions of the phase diagrams gases are more complicated. I am talking about transition lines to liquids and solids of course and most importantly about peculiar things that happen at the critical point. But what we consider as gas usually (e.g. air around us) can be treated as bunch of particles that don't interact almost at all. In other words, these particles are pretty much neutral.
On the other hand, plasma is not just about particles. Plasma consists of both particles and fields (usually an EM field but there are also many other types) and there are very complex phenomena that can transfer the energy between the fields and particles. This is a very important point as people often forget that fields are as fundamental as particles (more fundamental even, as according to quantum field theory (QFT) particles are just local portions of some field). So, from the point of view of QFT, plasma is a mixture of both matter and force fields. If we treated the system of charged particles + EM field on equal grounds it would be better described as electron-photon plasma. Similarly, there is a quark-gluon plasma (where the strong force instead of the EM force is dominant).
So, the main two points about plasmas is that they contain charged particles (under whatever force) and fields and that they are very complicated (due to being very dense, a necessary condition for breaking the neutral particles into their charged components). If we understood plasma well enough, we would e.g. be able to perform the thermonuclear fusion (at least in principle). This is currently not possible because plasma is very unstable.
Plasma is considered as one of the 4 fundamental states of matter. Charged particles must be close enough together that each particle influences many nearby charged particles, rather than just interacting with the closest particle (these collective effects are a distinguishing feature of a plasma). The plasma approximation is valid when the number of charge carriers within the sphere of influence (called the Debye sphere whose radius is the Debye screening length) of a particular particle is higher than unity to provide collective behavior of the charged particles. The average number of particles in the Debye sphere is given by the plasma parameter