A potential energy surface gives the molecular electronic energy, with nuclear repulsion, as a function of the nuclear coordinates under the Born-Oppenheimer approximation. Its minima describe stable configurations and its saddle regions help identify reaction barriers.
A reaction coordinate parametrizes progress along a chosen path on the potential energy surface. It usually combines several bond lengths or angles; it need not be one literal bond distance or elapsed time.
A transition state is the configuration or dividing-surface region associated with passage between reactant and product basins. In the elementary saddle-point picture it is a first-order saddle of the potential energy surface: stable against small displacements in transverse directions but unstable along the reaction direction. Transition state theory counts forward crossings and, in its simplest form, neglects recrossing.
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