what the heck is lift?

I have always been under the impression that lift is the product of
airspeed and angle of attack, and that lift is the measure of upward
force acting on the plane at a given time. For instance, if you are
doing slow flight, your wings are producing the same amount of life
that you would be if you were cruising, GIVEN that you did not lose or
gain any altitude during the maneuver.

My instructor, which is a very knowledgable guy tried telling me that
lift has nothing to do with airspeed. He said that lift is directly and
soley related to AOA and AOA only. So if you are doing slow flight, you
are producing more life than you are when you're cruising. I overheard
a ATP guy who flies King Air's say that this huge 20 ton military plane
he used to fly would fly approaches at 110 knots, and I heard him say
"It is able to do this because it producing so much lift", which I took
as him defining lift as my instructor does.

So whats the deal here? Are we just thinking of two diffrent concepts?