When you are lifting your friend's fridge, shoveling snow, picking up a heavy water cooler bottle, etc. - you don't care how much training effect you are getting. When you pull a one-rep max at a powerlifting meet or weightlifting meet, you aren't worried about how much stronger this one lift will get you. The goal is to move the object, make the lift, and do so safely and effectively. This is demonstrating strength.
In the gym, the goal isn't to lift the weight per se. The goal is to get stronger, so that when you demonstrate your strength it's there for you. It doesn't matter how heavy or light you go in the gym if you can't go heavy when you need to outside the gym. This is strength training.
Outside of the gym - maximize what you can do safely and effectively. Inside the gym - get the most out of your training, don't try to put the most in.