The two classes of receptors through which the neurotransmitters act are,
1). Ionotropic receptors
2). Metabotropic receptors
The ionotropic receptors allow the passage of ions through the ion pores. The ion pores selectively allow the passage of ions in response to the neurotransmitter released. Ion channels are very fast acting, which produce response within milliseconds, mostly excitatory
The metabotropic receptors allow the binding of neurotransmitters and produce responses that can be excitatory or inhibitory. They are comparatively slow acting, which produce responses within minutes to hours. The metabotropic receptors act through the release of second messengers (so, they are indirectly acting), and thus bring changes within the cell.