In #"homogeneous catalysis"#, the substrates, that on which the catalyst acts, is in the same phase as the catalyst. Often, this is not so much of a problem given that #"homogeneous catalysts"# are so active that can left in with the products of the reaction....and this might even apply to precious metal catalysts given that there is only a trifling quantity of precious metal sacrificed.
On the other hand, in #"heterogeneous catalysis"#, is in a different phase with respect to the substrates...and this separation of the catalysts from the products by simple filtration.
