One thing I never really understood until I almost got my CFI (Certified Flight Instructor) was the difference between how an airplane produces "Lift" and how an airplane "climbs."

Lift (To counter gravity) is primarily generated by the wings and is dependent on air speed, angel of attack, air density, surface area, etc.

Climb performance is based on the engine and how well the engine performs.

When I am really trying to make sure my students fully understand this fact I show a video of an F-16 in a vertical climb. I ask them what is the angel of attack of this jet vs us when we are cruising out to the practice area? If they say "The same" I go onto the next lesson. If they say "MUCH greater" than I know I have a little more work to do.