You are right. The terminology is confusing. Also frequently people get it backwards. The term load, when used relating to resistance, comes from a mechanical analogy: a SMALLER resistance generally means more current and hence a LARGER load. Conversely a LARGER resistance is often referred to as a SMALLER load. Confusing - I agree.
In any case with MM cartridges the issue is not current or voltage, the issue is to match the coil inductance and phono stage input capacitance with the correct resistance. MM cartridges have a very high series inductance, typically 0.5 Henries. The combination of the three values behaves like an RLC circuit, which under the wrong conditions will give a highly curved response (in fact an RLC circuit can act as a very effective band pass filter). The loading resistor is selected to dampen the response so that it is almost flat within the audio spectrum. Though there is always a residual hump in the response at around 10-12KHz. Therefore the load is critical, and not only that, the input capacitance of the phono stage is also critical.
As a general pointer, the input capacitance is typically around 250pF, larger values will reduce the frequency of the hump, but will decrease the damping, so should be matched with a slightly lower input resistance (maybe 40K Ohm for 330pF capacitance) I imagine that some sonic improvements could be achieved by carefully matching these values. So trying values of between 30K Ohms and 75K Ohms is a good idea if you have the option.
A benefit of using an MC cartridge is that the coil inductance is very low (around 20 micro Henries as far as I remember, I measured it for a couple of MCs recently, but I don't have the result to hand). So in the case of an MC cartridge changing the load / resistance does not significantly alter the frequency response within the audio spectrum.
Ironically though, you will see more discussion on the MC question. I believe that is because the people who spend $2000 on an expensive MC, are more likely to be serial tweakers, whereas Joe Public, who spend $200 on an MM, just wants to set it up and be done with it!
Hope this helps.
Brian