Lets use your example of an airfoil, even though it's not a 3 dimensional representation of the shape in question. Maybe this example will help you understand that lift is not solely an upward force.
The blades of an airplane propeller are shaped roughly like airfoils. Those blades, turning, create a differential force across themselves, which you probably refer to as "thrust", since it normally moves a plane forward, or in a direction parallel to the ground.
If that same plane were to accelerate vertically, perpendicular to the ground, those prop blades have now achieved lift. They're lifting the plane. How, in this sense, do lift and thrust differ?
Directionality. A matter of perception only. Forces are, in some cases, directly interchangeable with each other. If you follow the theorem of either Bernoulli's Principle, or Newton3, both of which explain aerodynamic lift, thrust, and several other effects which require differential pressure, lift is equal to the amount of thrust created in ANY DIRECTION.
Lift, in it's general use, which is apparently what you're referring to, is upward motion.
This is probably where we're getting mixed up. You're using terminology that my cousins in grade school understand, while I'm using terminology that requires at the very least, a basic understanding of physics and fluid mechanics.
I mean no disrespect by this, I'm only trying to figure out where the wall in our communication is.
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