Let down is a reflux action where your body will release milk upon stimulation of your nipples. When you first pump, you will notice a watery milky liquid. That is called foremilk. After this, milk will usually trickle off. Then the thicker milk will come in which is called the hind milk. This is the nutritious milk that the baby needs to grow. It will trickle off again and then come in again. Each time the milk comes in, it's called a let down.
When you express, you get 50-80ml milk. When you use your hand to press, is it before you express or after? I presume you stopped expressing after the milk trickled off? As long as your breasts are soft, means that you have successfully emptied your breasts. If you press, there will definitely be milk but it is not called a let down. During a let down, the milk just flows. You can't exactly stop it.
Babies are better at expressing milk than any pump in the world. And some babies will drink whatever amount that is given to them. So it is possible that she can drink 120ml ebm while you only pump out 80ml. If you dont't pump at regular intervals and stretch for some, it is also natural that you can pump more than 80ml because milk is building up. If you continue to drag pumping, your supply will drop because milk supply works on a demand and supply system.
She should be having 5-6 wet diapers daily. That should be the gauge as to how much she should be drinking that is enough. Poo poo ranges from baby to baby so that usually is not used to gauge if baby is drinking enough.