How is a stimulus transmitted across a synapse?

Omgg I'm learning about this in AP Bio right now too so let me explain:

So first you have neurotransmitters in synaptic vesicles behind the pre-synaptic membrane. Then, calcium ions go from the calcium ion channel to the vesicles to push them forward. The vesicles fuse with the presynaptic membrane, and the neurotransmitters are released. These neurotransmitters bind to receptors on ligand-gated ion channels on the post-synaptic membrane which causes them to open. Then, sodium ions go through those ligand-gated ion channels and continue the signal past the post-synaptic membrane. Then, the neurotransmitters go back behind the pre-synaptic membrane through the uptake transporters.