What is the definition of a Collisional Fluid? I am unsure whether this means the particles in the fluid must physically collide or does 'collisional' also apply to particles interacting in general, eg via gravity? I cannot find a good definition online/in my fluid dynamics book.
 A: In the context of particle scattering, such as between the constituent particles of a fluid, there's no difference between "physically collide" and "interacting in general": any interaction that causes a deviation from a straight trajectory counts as a collision.
Also, microscopically we don't have contact collisions, but rather, e.g., electric interaction.
A: In order to speak about fluid dynamics, there must be some mechanism that leads to local equilibration, so that we can talk about the local temperature, pressure, and fluid velocity. In a typical fluid (water, air, etc.) the mechanism for local equilibration is collisions between atoms, and as a result fluid behavior only sets in on length scales larger than the mean free path for collisions, and time scales longer than the collision time. 
In fluids made of atoms (or nucleons, or quarks, or electrons and positrons) we tend to think of collisions as microscopic, quantum mechanical, events that take place on a time scale much shorter than the collision time. This does not have to be the case. In principle the interaction can be completely classical, either a classical potential, or the interaction of particles with classical fields. The situation is simplest if the classical interaction is short range. Then the interaction time is short, and we can define classical cross sections and collision rates. Classical long range forces are complicated. A classical $1/r$ potential leads to collapse, and does not describe a fluid. 
There are many systems in which collisions are so rare that we don't observe fluid behavior. A typical example is a (dilute) space plasma. These systems are non-collisional plasmas. They exhibit some collective behavior, for example because of the interaction of particles with fields, but they are not fluids. 
This leaves the question whether there might be non-collisional fluids, that is systems in which local equilibration and fluid dynamics are observed, but there are no collisions. A typical example for this is superfluidity. We observe collective behavior and fluid dynamics, but collectivity arises from quantum mechanics, and collisions are rare.  
