MOSFET as a switch and Rds(on)

There are two common uses of the word "saturation" with respect to mosfets. Some people (the more academic types) use it to refer to the higher-voltage constant-current region. Some (more likely to be working engineers) sometimes use it to refer to the low-voltage ohmic region, like the bipolar transistor saturation region. That may explain the confusion.

Rds_on is the slope of Vd/Id for small excursions near zero volts, with some specified amount of gate turn-on voltage applied. It's less ambiguous to refer to this region as the "ohmic" region, and the higher-voltage part of the drain curve as the "constant-current" region.

John

There's nothing wrong with your understanding. "Saturation" has two different meanings, depending on whether you're dealing with bipolars or mosfets.

The Rds(on) when seen in a one line description of the part or on the first page of a data sheet - is "how low" in resistance "it can go" (like bragging) while saturated.

Then they give you curves to modify that figure based on temperature Vds/Ids, etc. with more realistic expectations.