Is a plasma a distinct phase of matter?

For clarity, there is a common misconception about plasma here. Plasma when being introduced for the first time to someone who doesn't know what it is, it is called "The fourth state of matter" which is an inaccurate description of it. Since this term is used for introducing some one to plasma, it is no big deal.

When a material changes from a distinct phase to another, it goes through a physical process called phase transition. When gas becomes plasma, it doesn't go through the standard phase transition. Hence plasma-in a general sense-can't be regarded as a distinct phase as solid, liquid and gas phases. It is a phase of the gaseous state. In certain rare cases however, transition from gas to plasma can be described as phase transition.

Plasma by definition is a mixture of free electrons and their ions (possibly negative ions). You need enough energy to liberate electrons from atoms. Roughly speaking, When you put that energy in a solid, energy might be dissipated as heat. If you put that energy in a liqued, energy might be dissipated in vaporization. If you put it in a gas it goes into breaking atoms and molecules (creating plasma). The following figure makes it clearer

Hopefully that was useful

Plasma is said to be a distinct phase because it does not observe the usual description and physical laws that are used to describe the usual 3 states of matter, on several counts:

• Plasma is not in equilibrium. Often it is far from an equilibrium. Therefore, thermodynamics can't be used to explain.
• Plasma is made of loose particles, but these particles do not follow kinetic theory of gases. Ideal gas law is not even a first approximation to model a plasma.
• Plasma particles do not follow a statistical velocity distribution (Maxwell distribution).
• Plasma must have two (or more) independent components. These components must carry charges. one is made of electrons, the other cations. It's electrons that are more active in deciding plasma properties.
• Unlike in gases, liquids, and (molecular) solids, plasma particles exert strong forces to each other.
• There is not a single temperature that characterizes plasma. This means two things. One, plasma is not a clear-cut phase, hence, there is not a clear-cut phase transition temperature, like melting or boiling, for plasma. Two, one temperature may not be enough to describe a plasma. The temperature for electrons may often be higher than that for the rest of plasma.
• Plasma can be confined by magnetic force (does not need a container wall).
• Unlike other 3 states, plasma is mostly unstable.

In the latter part, you have two questions which amounts to "What makes plasma a plasma?" Ionization is required to form a plasma, but there is no specific temperature requirement. Plasma can exist in interstellar space at around 100 K and in controlled laboratories at close to 0 K. The degree of ionization is usually represented as the ratio of charged ions to total (charged plus neutral) nuclei in a gas, and only a small degree of ionization (sometimes below 1%) is enough to make a gas behave like a plasma.

To be clear, a plasma is not the same as an ionic fluid, which is not a result of ionization but rather is made of cations and anions. Ionization means that electrons are set free from atoms or molecules. An ionic fluid is a salt in a liquid state.