Equivalent circuit of a non-ideal resistor
The difference is the parasitics that each model considers.

The first model ignores lead inductance but accounts for something like inter-winding capacitance in wirewound resistors. Interwinding capacitance is identical capacitance you get in inductors between the adjacent coils sitting next to each other and lets sufficiently high frequencies completely bypass the bulk of the inductor.

The second model ignores interwinding capacitance but accounts for lead inductance.

So really, a better (but perhaps needless complex model for most uses) is a combination of the two.


  
    It seems to me that the second circuit must be the correct one, since otherwise I don't see the point of ever using a speedup capacitor (the parasitic parallel capacitance basically acts as one). Is my intuition correct?
  


Why wouldn't you need still need one? Just because the parasitic capacitance is there doesn't mean it's large enough for your purposes.