Whats the difference between voltage gated and ligand gated neurons?
There is no such thing as voltage gated or ligand gated NEURONS. I believe what you are refering to are what is known as voltage gated and ligand gated ion CHANNELS. Each neuron has both types of channels in their cell membrane. 

Voltage gated ion channels open in response to voltage (i.e. when the cell gets depolarized) where as ligand gated channels open in response to a ligand (some chemical signal) binding to them.

Both types of channels are critical for proper activation of the post synaptic neuron. The pre synaptic neuron releases neurotransmitters into the synaptic cleft, these neurotransmitters then bind to the ligand gated channels, thus activating them. The ligand gated channels open up and allow the influx of sodium, which depolarizes the cell. This depolarization activates nearby voltage gated ion channels, which open up and let in even more sodium. Voltage gated sodium channels open up one region at a time, the previous region providing enough depolarization to activate the next regions voltage gated channels. This effectively allows the action potential to propagate through the cell.