The reaction coordinate describes the extent of a reaction. It usually corresponds to bond distance or angle. A transition state corresponds to the maximum on the potential energy diagram. Its lifetime is about a femtosecond. A reaction intermediate corresponds to the trough between the peaks of transition states on the energy diagram.
Lifetimes are much longer than transition states.
The Born-Oppenheimer potential energy surface describes the potential energy of a reaction complex as a function of the positions of the atoms taking part in the reaction. The saddle point corresponds to the transition state. Maxima are points of high potential energy, from repulsion between atoms. Minima are points of low potential energy. Enzymes hold reactants together in an optimal alignment for reaction.