To answer your question, it depends on how long the flight is. A commuter flight may use the same crew but a long-haul flight will get a fresh crew.
A shorter flight would mean that the cockpit crew has to repeat their pre-flight procedures. It’s basically a new flight when they take off again.
Yeah, I should have said drug and alcohol testing. They call it “DAMP” here, drug and alcohol management program or something.
Union rules along with governmental regulations govern the turn around times.
In the USA, unions are still pretty strong regarding this.
I can affirm that pilots are among the rudest people I’ve ever met, and I’ve worked with doctors and nurses and they are far worse. The joke is always, “They think 'cause they fly up there near God they ARE God.” 
The basic problem is they are very condecesing to the cabin crew.
I recall when I was the overnight manager in a hotel and we had a terrible pilot and he tells me “You better watch it or I’ll get my union and I’ll pull all the airlines business out of your hotel.” I told him, “Well you can try, but I know the airlines ALWAYS go with the lowest bid, provided the hotel meets MINIMUM requirements which we do.” And he just left in a huff.
Airlines are SO cheap and that has a lot to do with it too.