Is gabapentin a barbiturate or benzodiazepine?

Neither: It is an anti-seizure med. However, it may have some effects on the GABA receptor, though this may not be it's main mechanism of action. It can be sedating, like the other 2 classes of drugs.

Neither: Gabapentin works on voltage gated calcium channels to decrease release of excitatory neurotransmitters. Barbs/benzos work on the GABA receptor increasing its inhibitory function. Interestingly, Gabapentin was designed to work on GABA but in fact has nothing to do with gaba.

Neither: Gabapentin is used to treat partial seizures, pain related to post herpetic neuralgia as well as neuropathic pain. While it does modulate the activity of the major inhibitory neurotransmitter in the brain, gaba, it's mechanism of action is significantly different from that of a benzodiazepine or barbiturate. As a result does not result in physiologic dependence.