That is the only component of lift --- unless you think that Newtin's laws can be violated on a macro scale. But owing to the way that pressure is defined, the same phenomenon can also he understood in terms of a pressure differential.

this is just an argument in whether you want to explain the phenomenon mechanically or in terms of thermodynamics.

pushing a mass of fluid downward is equivalent to creating a net downward pressure. its the same thing, just expressed in different terms. the unit of pressure is force per square inch, for you americans. by integrating over all the area, you get the force that you are talking about.