Dave et al
From my recollection, some aircraft will have a slightly positive pressure for take off to avoid surging.
After lift off, the aircraft will generate a pressure schedule based on projected cruise altitude.. For example if on a short flight and say at FL250 (25,000ft) or below (will vary by type of course) it may maintain Sea Level/Departure level and then in descent schedule the cabin to arrival airport elevation.
As an example, LHR to AMS at FL230, aircraft will remain at sea level throughout.
If the aircraft flies above the level at which it can maintain SLP it will schedule a cabin altitude that maintains max differential pressure.
As an example, a B747-400 at FL350 (35,000ft) will schedule a cabin altitude at max diff of x psi which will result in a cabin altitude of, say, 5,600ft (ie below the 8,000ft maximum). If later on the aircraft climbs higher then max diff pressure will be maintained and the cabin will 'climb' higher. The cabin max of 8,000ft will be achieved only at the certified ceiling. Other types handling may be different.
On descent, a schedule will be started to get the cabin altitude to landing elevation usually changing the cabin altitude at a rate of ~350 fpm, so cabin altitude of 7000ft to sea level takes about 20 minutes. This equalises the rate of change the ears have to endure.
I once had a problem with the rear outflow valve freezing in the almost closed position on a B737 and none of the control modes worked. This resulted in max diff press being maintained, so as we descended so did the cabin to well below sea level. When the temp increased the valve unfroze, which resulted in a VERY quick pressure change equal to an instantaneous climb of several thousand feet! Not fun on the ears, although better on the tubes to have a climb rather than a rapid descent!