What is the definition of Lift? Lift is a term that is used very frequently here, but I cannot find any post explaining what it is exactly. I am looking for the exact definition of lift, not an explanation of how it is generated.

It seems a very simple question, but I have not been able to find consistent answers to it. Some very well respected sources even contradict each other:

At https://en.wikipedia.org/wiki/Lift_(force) Lift is defined as:
A fluid flowing past the surface of a body exerts a force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction.

But according to NASA (https://www.grc.nasa.gov/www/k-12/airplane/lift1.html):
  Lift is the force that directly opposes the weight of an airplane and holds the airplane in the air.

If a plane is flying straight and level (at constant altitude) these definitions are the same, but otherwise they are not the same at all. So, which one is correct?
It's the component of the aerodynamic force perpendicular to the direction of the air flow, the aerodynamic force being the reaction of the wing to the relative wind.