Stopping the urge to vomit
Vomiting is a reflex run from a control centre in the brainstem. Several inputs can trigger it: a chemical sensor that samples the blood (the trigger zone), signals from a churning gut, the balance organs of the inner ear, and even sights and smells. Each input speaks through its own messenger — chiefly dopamine, serotonin, histamine and acetylcholine. An antiemetic works by being an antagonist at one of these messenger's receptors: block the right one and the reflex never fires.
This is why the cause matters. Motion sickness comes mostly through the inner ear, so antihistamine-type and anticholinergic drugs help. Sickness from chemotherapy floods the serotonin pathway, so a serotonin-blocker (the "-setron" drugs) is the right tool. Drug-induced or post-surgery nausea often runs through dopamine, so a dopamine-blocker fits. Matching the antiemetic to the trigger is far more effective than picking one at random.
Speeding up and slowing down the bowel
Lower down, the problem is rhythm. A laxative relieves constipation, and the gentlest kinds work by simple physics, not by forcing nerves. A bulk-forming laxative is fibre that holds water and gives the bowel something to push against. An osmotic laxative pulls water into the gut so stool stays soft. A stimulant laxative does prod the gut wall to contract — effective, but the one most likely to cramp if overused.
When the bowel runs too fast, an antidiarrhoeal slows it. The common one is an opioid-type drug that acts only on the gut's nerves, calming the muscle so contents linger and water is reabsorbed. The key honest point: in many infections, diarrhoea is the body flushing out the bug. Slowing it can keep the infection in, so antidiarrhoeals are for comfort in mild cases, not for high fever or bloody stools.