It's cool that professor can write backward, and I read some definition (e.g. Maliva, R.G., 2019 ) is "unsaturated zone=vadose zone + capillary fringe"
Is there an identifiable and separate "saturated zone?" No - there can be perched regions that have saturation that are surrounded by unsaturated soil. So please remember that the notion of breaking the wold into "saturated" "unsaturated" "vadose" and "critical" zones are imprecise expressions when applied to large volumes of material. Locally, it is more accurate to discuss saturated and unsaturated locations, but as a "zone" it can often be imprecise.