Parasympathetic stimulation is a process that takes place in the peripheral nervous system. This is a process where signals are carried throughout the body.
Parasypathetic division
Pilocarpine is actually a Muscarinic cholinergic receptor (mAChR) agonist. It works on the Parasypathetic nervous system; therefore, it makes sense that the agonist working on the PNS would result in decreased heart rate. Atropine, in contrast, is an muscarinic cholinergic receptor antagonist and will lead to increased heart rate due to the lowered effect of the parasympathetic system on the heart.
The sympathetic nervous system is also known as your "fight or flight" nervous system. It's a fast acting reaction. Imagine that it's dark, late, and your walking home alone and you hear an unexpected sound closeby, your sympathetic nervous system kicks in as a response, your heart starts pounding and your body prepares for what's next by producing more glucose and therefore more energy so you are ready for what is coming. The parasympathetic system is the resting nervous system. This system is slow-acting and for actions like digestion. When you eat a large dinner and your sitting down feeling relaxed and full, your parasympathetic nervous system is working hard to keep your body regulated and in homeostasis.
the autonomic nervous system (ANS) includes the peripheal nerves and ganglia on either side of the spinal cord ( note: some textbooks include the ANS as a division pf the peripheal nervous system both ways are correct.)
The parasympathetic nervous system (PSNS) is one of the two main divisions of the autonomic nervous system (ANS). The ANS is responsible for regulation of internal organs and glands, which occurs without conscious effort. The parasympathetic system includes the normal regulation of bodily functions, while the sympathetic system is concerned more with rapid reflexive and instinctive reactions.