...I would say that the critical change is that in decompression diving the return to surface is generally triggered by reaching a planned time limit, whereas in "no-stop" diving the return to surface is often triggered by reaching a planned gas limit.
I often dive with a club that I am a member of. Depending on the number of people who show up for a dive affects the format of the dive and what gets briefed...for instance (some possible scenarios):
A) if it is just 2-3 people the plan would be to stay together throughout the dive as one dive team, obviously.
B) if there are 4-6 people who are familiar with the dive site the brief may state that each pair of divers would be a team and the brief will also specify that the teams will dive as a loose group but if a pair become separated the dive will continue...or it may be briefed that each pair will do their own dive.
C) if among the 4-6 people there is not enough divers familiar with the site for each pair to have someone in it who is familiar, then the brief would be the group will stay together...if a pair gets separated from the rest lost buddy protocol would be enacted.
D) if the there are more than 6 people, this is way too many people to keep track of typically and it is incumbent on the buddy pairs to stay with the group, follow their own dive plan, or follow another pair that is familiar with the site.
Regardless, we brief maximum depth to not exceed and maximum dive time. The expectation is that if you end your dive because you burned through your air in a short amount of time, you will wait at the briefed point of egress until the rest of the divers finish their dive....the rest of the divers who are more efficient on air or who are diving a larger capacity tank are expected to be at the surface at the egress point by the specified maximum dive time regardless of how much air is left in their tanks. Everyone returns to the cars together. If there is an issue, such as it is cold and the wait is short, the expectation is that the divers will grin and bear it...if the wait is long then one diver from the pair that surfaced waits at the egress point while the other runs back to the car to get warm clothes on or whatever then they come back and the other dive goes to take care of whatever business they need to tend to...but there is always someone at the egress point representing that buddy pair.
(of course, if an emergency scenario develops that takes precedent)
When diving outside the club type environment, then I agree, the dive time is usually limited based on air consumption or comfort....I have aborted dives with plenty of air because it was just too damned cold below the thermocline at the site and for whatever reason my tolerance was not up to grinning and bearing it on those occasions.
-Z