The important thing about catalysts is that they are recovered at the end of the reaction in their entirety, they are not used up during the reaction. They often undergo a temporary change during the reaction, but are turned back into the original chemical at the end of the reaction.
Catalysts change the rate of a reaction, but do not alter the position of equilibrium.
Although the yield within a short time seems more, the overall yield from the slow reaction would eventually be the same, but as it can take ages to get that far we usually don't wait that long.
Transition metal catalysts are either homogeneous catalysts or heterogeneous catalysts.
Homogeneous catalysts are those in the same physical phase as the other reactants e.g. all in solution together in the same solvent, or all are gases.
Heterogeneous catalysts are those in a different physical phase to the rest of the reactants. E.G. two different liquids in contact with catalysis occurring at the interface between them, or more commonly a solid catalyst and a solution, or a solid and gases.