What is the difference between a presynaptic neuron and a postsynaptic neuron?

Neurons transmit impulses  from one neuron to the next neuron across the synapse. Said another way, the synapse is where neurons meet each other, chemicals called neurotransmitters fuse across the synapse. These neurotransmitters are necessary to convey the nervous "message" from one to the next. The answer to your question is just of location. Anatomically, the presynaptic neuron is the neuron before the synapse, this neuron is delivering the "message" across the synapse to the postsynaptic neuron. The postsynaptic neuron is the "receiver" of the neurotransmitter "message". Again, the difference is just one of location with one sending the chemical message and the other receiving the chemical message.