Socio-economic question

Given a colonization mission that is essentially totally divorced from the homeworld, e.g. somehow a small but viable population made it to Saturn, or the Oort Cloud, or Lalande 21185 and grew in subsequent decades and generations how would or could they transition from the crew of astronauts/cosmonauts/tychonauts with One Ship-One Captain-One Law and The Mission to a society ?
When and how do the explorers become settlers, and what will the settlers pass on to their posterity ? I'm recalling Clarke's Songs of Distant Earth, Poul's New America plus works by Niven, Varley and others.