Yes, benzodiazepines do indeed act on the GABA (Gamma-Aminobutyric Acid) receptors in the brain. Specifically, they bind to a particular subtype of GABA receptor known as the GABA-A receptor. When benzodiazepines bind to these receptors, they enhance the effect of GABA, which is an inhibitory neurotransmitter. This enhanced GABA activity results in sedative, anxiolytic (anti-anxiety), anticonvulsant, and muscle relaxant effects.
Pregabalin also has an effect on GABAergic neurotransmission, although it does so indirectly and via a different mechanism. Pregabalin binds to a protein known as the alpha-2-delta subunit, which is a part of voltage-gated calcium channels in neurons. This binding reduces the release of certain neurotransmitters, including glutamate, noradrenaline, and substance P, among others. Although it doesn't bind directly to GABA receptors, the net effect of pregabalin also results in reduced neuronal excitability, and it is used for some of the same indications as benzodiazepines, such as anxiety disorders, epilepsy, and neuropathic pain.