What is the main difference between stopping and skimming when plastering and when to use each
Skimming probably does come from before plaster board became ubiquitous. Previously you'd apply a coat of undercoat plaster to the wall or laths and then a top coat to finish. You'd also skim a new coat of topcoat if the wall had been damaged beyond simple filling. A good plasterer would be able to get a glass like finish on this topcoat with no sanding required.

Skimming over plasterboard gives you the same options. You can get a good finish without sanding - which is a messy job.