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)
As electrodynamics is involved, plasma can diffuse much faster than a gas, if there is an electromagnetic field applied.