I believe you've got the general understanding...
Turn the altitude knob and 'Pull' will give you either climb / idle thrust as appropriate and the aircraft will ignore all constraints.
Turn the altitude knob and 'Push' will give you a climb / descent along the profile calculated in the FMC, which includes any constraints you have programmed.
The 'dashes' on the FCU will never appear in the altitude window, because despite following the profile you still have to give it a hard height to climb or descend to. There is a circle that appears next to the number on the FCU which indicates whether the active mode is managed or selected.