There are three sets of particles, one looks like fast watery spray, another like flames, another like smoke - I tweaked material properties and animated textures until they each looked decent, kinda using a built-in 'fire' effect as a starting point, and coded events where one particle type would emit another, how the velocities would conserve, and all that stuff that makes the spray actually 'catch on fire' before it 'burns up' and vanishes, and makes the fire smoke as it dims and dies. The fire is "focused" by a force field that pulls it towards a flame shape instead of a cone shape, and the smoke particles react more to wind and air turbulence fields, as well as losing momentum quickly and rising in the air (as opposed to flying through the air like a ball).
I'm sure 3D Studio Max has particles in it somehow or another, but you might have to get a plugin to get them, and that might get expensive... I really don't know!

3D studio in the past used to be cheap compared to Maya, and came with a very basic feature set that made you get plugins (sometimes plugins were $600!) to get the missing features.
for example, get the full version of Maya, and you get subdivisions modeling (Geri in the Pixar short Geri's Game was modeled in subdivisions), a dynamic cloth simulation engine, an animal fur shading engine, an organic plant-life creator called Paint Effects, and a bitmap-video motion tracking engine that will determine the 3D locations of objects and cameras in a video feed, so that your 3D stuff will seamlessly blend with the real scene, as well as the basic polygon and nurbs modeling, volume primitives, particle system, skeletal animation system, and rigid and soft body dynamics (think animating a bowling alley or break on a pool table, or a Koosh ball hitting a wall). But you pay $7,000.