This question is a bit tricky, but the simplest answer is that neurotransmitters are the chemical transmitters in the brain. Drugs are typically designed to increase certain neurotransmitters, which leads to a reduction in anxiety.
However, the neurotransmitter GABA is an inhibitor (a natural one) of the fear response, and when certain drugs are taken that affect GABA, they actually lead to increased inhibition of the fear response.
To make this clearer, think of endorphins, the body’s natural painkillers. When you get hurt, endorphins are released in your brain to decrease the brain’s ability to process pain signals.
If it is not enough, we can take a pain medication that will have similar effects (as if we were to add more endorphins to our brain chemistry, or somehow make those endorphins stronger). GABA is similar to endorphins, but it works on the fear system, and certain drugs make it work even more.
We are still learning exactly how all of these chemicals work in the brain. This is partly because of the vast complexity of the brain and partly because we are limited in the types of studies that we can do with humans, we cannot actually go into the brain and observe it working.
Just how dopamine, GABA, serotonin, and any other neurochemicals exactly work in the brain will be the subject of much further research, and it will most likely take decades before we can reach any firm conclusions.