There seems to be a direct correlation between all of these elemental damage types present in the roster, except for Toxin, which is just added because it's one of the basic elemental damage types.

They're all sub-molecular. forms of energy, energy transferral and physical constants.

Impact = direct kinetic energy transferral. (puncture and slash are only observable on the macro scale, when an element is actually formed)

Heat = Atoms accelerate due to the magnetic force inherent to them, also pulling them together.

Cold = Atoms decelerate due to the kinetic force they impair on other atoms and similar objects.

Electricity

Magnetic = magnetic force.

Radiation = the purest form(s) of energy (that we are able to utilize in a "controlled manner")

However, the line up for the progenitor frames is definitely arbitrary, probably due to the fact that DE wants to keep at least one or two progenitors that basically everyone and their grandmother can just go and get right then and there.

Rhino for impact,

Ember and Inaros for Heat,

Frost and Titania for Cold,

Almost the entire electric Progenitor Frame roster,

Ivara and Oberon for Toxin,

Mag for Mag,

Ash and Loki (maybe Mirage) for Rad.