Actually, I'm looking at an International Rectifier IRF7201 datasheet, and it appears that around Id=5A, Rds~=.025 @ 10V and ~=.035 @ 4.5V. That seems like such a small difference. However, as Id reaches around 20A, the curve for Vg=4.5V appears to spike up exponentially, while the 10V curve remains flat.
It's a 40% increase in resistance, which means a 40% increase in power dissipation. Might seem small, but it's all about percentages here.
Would it be corret to say that under 20A, the device is "fully on" with VG=4.5V, but not at Id>20A?
Correct. Drain-source current does have an affect on the channel resistance. Although I don't know the exact details as to why. Yet.