Being oily yet dry at the same time and hydrating vs moisturizing
This one is tricky indeed... The thing is that lack of oil (damaged lipid barrier in skin) leads to dehydrated skin, so in practice the difference between dehydrated and dry skin is actually not very helpful. To moisturize/hydrate the skin properly, we need both humectants (attract water) and emollients & occlusives (help to keep the water in) - at the same time. If skin is oily, a lighter textured moisturizers might feel better, but they still need to include emollients to work properly (moisturizers for oily skin often rely on silicones for emolliency). Applying hydrating products without emollients can actually lead to more dehydration, because humectants in them can attract water from within the deeper layers of the skin & increase its evaporation.